The number of people I see riding bikes in normal clothes (ie almost every single one) would suggest that is not an issue
My point is more about the perceived barrier to riding bikes, rather than those already doing it. We seem to have a conflict in the UK: increasingly we see movement in favour of a more Netherlands/Belgian/Danish style of bike usage, but at the same time create an entry restriction in the way cycling is sold as a “healthy” in the same way jogging and gym membership is.
Mind you, I also have views on the prevalence of mountain bikes, rather than sit-up-and-beg dutch style bikes, as a hindrance to more mainstream cycling.
(As it is, my commute used to be 17 miles each way, so i wore cycling clothes (rather than my suit) and ride year round. New commute (as yet unridden) is 15 miles each way. I’ll still wear cycling clothes. Were it 5 miles or under, I’d wear normal clothes.)