This topic is a blessing. I have an anthro character in my story and I've been thinking about public's reaction for some time.
I don't consider myself part of the furry fandom neither and I made a great effort to make my character look more animal than human (that's the kind of anthro I prefer). I can assuredly state that it took me 1 entire year to develop this character - and I'm still putting the finishing touches. One of the strongest references to its design was Shirokuma Café, in which the caracters [that aren't human] are 100% animal, no middle ground.
Altought I prefer characters that are more animal, I must say I like some on the other way too. Actually the greatest problem about this, in my opinion, is the approach. Overly sexualized anthros? NO. Ultra happy Disney-like mega colorful anthros? LOL NOPE. Kid-like overly sexualized Disney-like mega artificially colorful anthros, having sex? [deep facepalm]
Anyway, I'd like to share some references with you here to base some of my opinions. For example, starting with an illustrator I admire a lot, Jerome Jacinto. He can draw more animal-like anthros, like this one, a middle ground, and anthros with human shaped-body but with stronger animal characteristics, like his latest illustration and they're still great imo. He knows how to give an appropriate approach to them, as well as he knows his craft very well.
Another illustrator that draws animal characters is J. T. Cole. Sometimes they're more animal, sometimes they have a human-shaped body, but with strong animal characteristics. Take a look at this, this and this.
And there is a webcomic that was not mentioned here that also has human-shaped characters with strong animal traits and that has a good approach, that is Beyond the Western Deep. And guess what, Jerome will draw the next entire chapter of the comic!
Oh, about Shirokuma Café...

It's great for references!