It depends about how heavy is the accent... If it's really too much heavy, then yeah, it can turn me off.... But when I hear mid or slight accents, I don't care, and especially more if the voice appeals to me ♥ If the voice is interesting and such, I don't mind if it has a slight or mid accent, justly that adds some colour and uniqueness (your mileage may vary) to it without screwing up understanding.
After for me personally, I won't deny it... I tend to fear accents on MY banks... Even when some don't find it heavy or hear it but find it cute, I'm still like "yet I feel it's heavy ;w;"... Because 1) I'm perfectionnist despite the lazy-cool impression I can give 2) I'm deeply scared of people's judgement and I'm even more afraid of not being understood... When I see people being truely picky with either Japanese or English (because yes, people can even push you down for English) I feel like I'm horrible and it makes me feel like I'll never be considered as someone who's able to speak/sing differents languages and so would do my UTAUs... I mean, for those people, it seems like "Not having any accent AT ALL + good pronunciation = perfect/good/you sound really like a Native or like a speaker MUST be"... And the worst is that it sadly seems to be the only formula to be perfectly understood for all of the ones picky with accents... So yeah...
I try all my best to hide it and to try mimicing the aimed-language's tone... But nothing to do... It keeps showing, no matter how much I record, how many times I do it again over and over until my voice breaks, how much I'm training more and more...
So yeah.... When it's the others, I don't care (except if as I said, the accent is truely huge and make the voicebank sound too much weird or not enough understandable) but when it comes to my own banks... It's like the end of the world when I cannot make them sound like Native's ones would do... I fear people refusing to use my banks or to give respect because I don't manage to sound as Native as them... And if I am too harsh with myself when it comes to my own banks' accent, it's also the fact that I want to break, by managing to finally reach a Native-like sound, this ****ing prejudice about people of my area's way to speak languages...