If you want to hold others to those expections then do the same. That may cut your repertoire by 75% maybe in some cases for some people 90%. For me I'd be shit out of luck as I have a very thich Bostonian accent & I don't have any local songs that I can do in that accent. I can do some NYC folk songs but my Brooklin & Bronks accents suck so under these guidlines I can't even do those. There goes my repertoire of cowboy songs too. I do a lot of shanties, but I've yet to hear many/any who talk & sing like the few old deep water sailors that I've met & heard who've spent their lives at sea. I sing a bit at the sessions I go to & some of the singers are Irish some not but if the singers are good it makes no difference where they're from they keep getting asked to sing, all the time.
Me, I'm content to do as I do, I haven't heard any complaints about my accent. Maybe it's a personnal thing for you & you should keep it that way. You'll be sticking close to home though & you'll be cutting down on the music intake too.
Good Luck
Barry