I am shocked that this isn't a topic already. '_' It's something you hear all the time, especially in trope talk...yet it's never been focused on. Okay, then.
So, "relatability"...like I said, it's been mentioned a lot already, often as the #1 excuse used by people who write bland, uninteresting characters (harem anime protags, YA novel MCs, etc.).
I put it in quotes because it's really a false, almost oxymoronic concept...a truly relatable character and a character that you can pretend is you are not actually the same thing. Sometimes those descriptions overlap: for instance, when you find a character that is so much like you, watching them move through their story, enjoying things you enjoy and making decisions you might make, is like watching a version of yourself in a parallel universe.
But the instance so widely cited is usually when you find a character that is so empty and devoid of personality/motivation that you can simply "fill in the blanks".
When they decide to go out with the love interest, it could be because "he's SUUUUPER hot, omg I WANT HIM" or because "I might as well; I've never had a boyfriend but since he's here...".
With the blandest, tropiest examples, the only overt reaction you see is usually something in the middle of those extremes (like
"...Okay") where you can apply whatever internal reaction you want, like the ones above. And this just...keeps happening, for everything they do. They become "relatable" simply because no evidence is presented to the contrary.
...Except, of course, for those people who don't fit the stereotypical average that these "relatable" MC's are supposed to represent (i.e. white cishet upper middle class youth). I feel like I've mentioned it before, but it's even more surreal to watch people go "they're not bland, they're relatable!!!1!1!!" when you can't even imagine doing some of the stuff they do, like...I dunno, going to a mall and buying things just for fun.
Relatable to whom?? Couldn't be me....but honestly, that's worth a topic by itself. ^^;
I guess things like that are part of the reason why I would say "not much" in answer to the titular question. When you're not included in that stereotypical average, you get used to seeing characters who are nothing like you all the time, and the idea of needing to relate to enjoy something isn't as strong. You may still wish to see someone like you as an MC, but your knee-jerk reaction to seeing someone who isn't is not "who the f*ck is this"...or the more subtle "tsk tsk; they're unrealistic". You just go with it. =/
And from a writer's standpoint, I'd say "not even remotely important at all", although that's just how I am. I've more or less abandoned the idea of being able to present my work as "relatable" to anyone, much less the masses...so I just focus on letting all my characters be themselves. I can't imagine tailoring an MC to appeal to anyone besides me...especially if that meant ripping out everything that made them unique (this is why, although I love character design with all my heart and soul, the idea of doing it for a living is lowkey horrifying).