When the cover image/promo art is full of female characters, but the summary says that the main character is a guy. Huge red flag for me.
To me that says that the female characters are probably just being used for sex appeal, or to draw people into an otherwise boring and uneventful anime. And I know that's not always true (Rozen Maiden is pretty amazing~) but 9 times out of 10 it is, because "CUTE GIRLS" is just easier than writing a decent story. Well, I ain't got time for that.
Fan bases.
It really pisses me off that I do this too cause I SHOULD be able to ignore the fans and just enjoy the series itself, but it's just REALLY hard to enjoy a series after you have been harassed to hell by it's god damn fans.
Heck, this extends to even stuff I create, where I will hate working on a story anymore because the fans are just horrible and have ruined any enjoyment for me.
MLP, Voltron, Steven Universe, Kuroshitsuji, AOT (actually no scratch that one... that was a little different, the fanbase attacked me for NOT liking that series cause you are apparently NOT allowed to not like that series) all examples of series I enjoyed when I first saw them but had trouble continuing to enjoy because the fanbase attacked / doxed / harassed me cause I liked the wrong character or ship.
My number one reason would have to be fan bases. Now, this reason can be flexible. If the fandom ends up getting smaller over time/a lot of people leave it and the fandom becomes inactive, THEN I might consider joining. But usually what steers me away from series is the fandom because:
A. People are toxic to each other, because apparently not liking a ship warrants a death threat.
B. People are toxic to the creators, because apparently not making a ship canon warrants a death threat.
C. Too much drama -- which is A and B all rolled up into one PLUS some more. Rumors/Scandals about content creators, the actual shows' creators, blah, blah, blah. Like, if all I see if drama when I'm trying to search for the fandom, even when I use very specific tags to get AWAY from it, I just can't. I'm dropping the series and leaving it for another time, if I ever decide to come back.
My only exception to this rule will always be Tite's Kubo BLEACH because most of that drama is about the Bleach ending and the ships (IchiRuki versus IchiHime), and I can easily bypass all of that bullcrap with ease.
My smaller reason? -- Boobs and Gore. This is more specific to horror anime/manga series, but I will just drop a series if there's this weird combination of nudity and gore. If it's not someone getting murdered horribly, every. other. panel. is some shot of a girl's panties, cleavage, or some weird pose she's in for some reason showing BOTH. Lord help me if they show her exposed WHILE getting murdered. Hell, even a lot of the horror slasher movies don't amp it up like this.
Love at first sight makes me drop the comic instantly, like especially if it happens within the first few pages as soon as character A and B look at eachother (I dont like attraction at first sight either).
Honestly im fine with a variety of art styles but what i cant get past is terrible colour choices, i dropped a comic bc the one of the characters had the most horrible shade of green as a hair colour.
with comics,, bad fonts???? and like, "each character has their own font" type deals.
ugh, i just, can't read those. it's a huge distraction from the story for me
with series (anime, "normal") it takes a bit more to get me to quit but if i don't like the way the main actors looks (especially things like piercings, i dont know why, can't stand it), or "all toddlers" series where everyone's a college kid or younger like. listen, im gonna need some characters who arent striaght up children (*sidenote 'all toddler' series applies more to normal ones than anime because almost all anime is all-toddlers)
with anime i also almost always avoid self-describing "horror" anime becuase it never, ever lives up to the expectations and always feels very lukewarm. id rather have my horror in manga form where there's a lot less limitations lol
The "BL" on the thumbnail.
I don't hate the BL genre, I allergic to that word on the thumbail because it's everywhere!
There is no need to put the" BL" onto thumbnail, when your comic is in the BL category!
A cookie cutter art style or slow pacing. Like a typical Manwha style that doesn't go beyond just readable for me or just a blatant Steven Universe, Cartoon Network or Adventure Time copy because they're relatively easy Art styles to copy, hell a middle schooler can do it. It's not like I just can't like it when somebody does their own thing with it (Look at Spire, it's bloody amazing.) Also, slow pacing reading one page a week is kinda a killer for me because these people aren't gonna make progress anytime soon. They can spend the better part of a year writing an acceptable fight, so I can't help but drop things in that format. I rather get 10-12 pages a month in one bite rather than a grand total of 4 spread out.
I usually don't let small things(amateurish art style is the exception) derrail me from at least trying a story, although the one thing that makes me drop a series harder than an eminem diss track are dumb/selfish/bad characters. I remember dropping this one series about a potion selling girl cause she acted like an entitled shit to the god and the whole world were idiots that would just bow down to her superior intelligence 
said the same thing until mi sister told me she got use to it in the end(it becomes white noise after a while), and thank god I listened cause in the end they actually gave a legit story reason for the fan service and why less clothes are better than fully clothed XD
OH my gosh, yes! Especially if it's the protagonist!
They're the biggest assholes on the planet and people rightfully do not like them. But we're supposed to set aside that "in your face" fact because they can save the world or something. I see it rampant in a lot of manga where protagonist is just full on groping people out of the blue, but "hey, they have the powers to save the universe and defeat God, so it's ok!" Big reason I dropped them.
I rather prefer it when the author is out and about with the fact that their characters are assholes and playing with how that can interfere with their journey or how it affects their surroundings than trying to justify the behavior and convince readers to turn a blind eye to it.
sounds like most wuxia manhuas if I'm honest, also the reason why I don't like most wuxia manhuas, their too "might makes right and if you don't like it then you must die"
I used to watch a lot of anime as a teen but nowadays, I avoid it. Mostly because I hate the modern anime art style. Heck look at the OG Digimon vs the new one, they all look so bland. I also can not stand moe/loli characters, which have blown up in popularity over the last 10 years. Anime feels too much catered to otakus now. I feel alienated watching modern anime.
I also hate realistic gore and mutilation, it makes me uncomfortable. i can tolerate Super Jail but not those Tru Crime shows.
I also dropped that new Sabrina show like a hat when they started mentioning Satan and Satanists. It feels like it was written by those paranoid christians who think witches equal Satanist. It also lacks knowledge that most modern Satanist don't worship the devil and are more of an anti-Christian group that fight Christian groups who abuse laws. Most modern witches/neo-Pagans are peaceful. I know there are the neo-Nazi pagans, but this show wasn't really talking about them.
Usually, it's something like this:
"Wait, is that main character a tsundere? Okay....puts on jet pack BAIIIIIIIIiiiii."
Or if it's the same rehashing of "Brown Haired Boy gets Rainbow Harem"; one look and I'm out ^^;
on the other hand, sometimes I'm so petty I will watch the whole thing, or at least the rest of the season, just so I can effectively tear it apart when the time comes XD
So I know RWBY is very popular but I have never been able to watch 10 seconds of it because I HATE the animation. It's so stiff and off putting to me. It makes me cringe. 
Oh yeah, I have the same issue with that series especially 3D, also has this same issue with Dragon Prince, the animation was just not fun to try and watch at all. (Though I finished watching Dragon Prince, as it was much shorter and I was watching with other people who were interested in it)
The story and characters themselves put me off RWBY, tbh. I can deal with the weird style and the one great thing it has going for it is the fight scenes, but it's not really enough to slog through how horrifically 'anime' it all is to get to them. x_x
This reminds me, when series will hamfist in pop culture references that are so blatant and awkward. Just to be like "Haha look how hip and cool we are, we know what a meme is!" It's so weird too, because you know in a few years it'll be dead and people watching later will have no idea what the characters are talking about it. I dunno if that was also part of what you meant though.
I saw a ton of criticism hating on She-Ra's design for being too 'masculine'. I don't really see what they're seeing but I agree with this, overall cast designs are very bland and lacking some kind of dimension. Clips / trailers from the animation put me off watching it though. Ooooh boy, there's a lot of basic drawing fundamentals missing here in all the scenes. There's just a line where it's way too obvious to not keep noticing and it breaks immersion. @_@
I don't know about such tiny things. I drop series usually because serious reasons like:
- When they produce a half hour inner dialogue about their dilemma and also their backstory during three sec fightscene...
Attack on Titan could do this... They over-dramatized everything. Oh god how I hated that series. 
I can not point out a good element of it. I gave a chance to it because everyone loved it but I could not bear more than some episodes. It was a main reason I did not start to watch animes again. I don't consider myself as an animefan anyway. There are more things I hate in anime than I like.
- Bonus: when the 3D animation FPS does not match with 2D animation FPS... It kills me.
For me it totally depends what I went into it expecting. For instance I don't mind fanservice, even excessive fanservice because sometime I fanservicey comedy is just fun, as long as they're up front about it. If you're going to go "this is a super deep dark story we want you to take it seriously but also omg look boobs for no reason" it's not going to work. For instance Cross Ange is a pile of beautifully animated and voiced fanservicey trash but if you know that from the very start and doesn't pretend to be otherwise and if you can tolerate that there's actually something of a half decent plot under there. But if I watched Handshakers because it was billed as much the same team as K which I adore (the decline after S1 of that should have clued me into how this was going to go) but I couldn't get passed episode 1 even after several attempts, the animation was an awfully obvious 3d, the boobs were huge, the jiggle physics were awful and was the girl making sex noises in battle really necessary in a show you're trying to tell me is serious and threatening?
Although the pettiest reason is probably because my friend insisted something was "the best show ever" in all seriousness and then that she'd "never connected to a character like this before" about the villain in all seriousness, without a hint of irony or joke, and then said she couldn't be friends with anyone who didn't like the show it was so important to her. It was already dragging as a show, but it had potential so I was sticking, but after that I dropped it so fast.
I don't necessarily drop many series, but I do find myself struggling when characters start monologuing about their motivations really sentimentally. Not only does it slow down the pace, but it also ruins the fun of watching a character's actions and figuring out their personality from there.
I know the first episode of Darker than Black did this, if any of you have watched it. It was an alright show.
