I think it is more of a problem in the US, given half a chance Trump would make homosexual relationships illegal. Having said that of course there are a lot of anti-gay freaks here in the UK, especially among extremist theists. But gays don't seem to fare quite so badly in the UK as they do in the US.
It is very difficult to make direct comparisons between the UK and the USA because imo we express ourselves in totally different ways. So (and I am speaking in generalities here) Americans are much more upfront.
For example last year I had some American friends over, one of whom is gay (although happily married to a woman, another story for another thread perhaps) and we went to Chester for a break where one evening he got quite merry and in the hotel bar told us about his experiences growing up gay in New York and being around at the time of Stonewall. He did this very loudly and uncompromisingly to my ears. I would suggest most gay people in the UK would be more circumspect about how they talk in public.
So in the US a forthright exposition of views is I think much more likely to create a similar forthright reaction in anyone opposed to you.
In addition we make the mistake of thinking of the US as one country. In many ways it is not and attitudes vary greatly between different states, and indeed between different areas within individual states.
Also I think it is a mistake to think that the "metropolitan" view of sexuality is widely accepted in the UK. Doncaster (other options are available) is another country compared to London.
In short, the British, most of the time, hide their prejudices behind a veneer of civility.
The Americans don't bother with the veneer.