It is absolutely a stretch in my opinion.
In my own experience, living in the U.K., I found it so much easier to come out as gay than I did as trans ( I come out as gay before coming out as trans). I was much more accepted as being gay by more people than I was for being trans.
Acceptance of Trans people is way behind acceptance of gay people in this country, arguably throughout western cultures, in my opinion.
I realise that my experience is annecdotal however.