That statement alone will divide customers in the U.K. and the advantages/disadvantages of withdrawing from EU human rights agreements are something that reasonable people disagree on.
Generally supporting established lgbt rights with no specific link to policy is different - it’s overwhelmingly supported and not even generally classed as a political view anymore (along with “is evil bad?”).
You're missing your own bias. There are people in the US (and in the UK, in the Vote Leave team who are now in Government) who believe that LGBT people (in particular the T) shouldn't exist.
LGBT rights are human rights. Brexit absolutely has a human rights component to it.
Generally supporting established lgbt rights with no specific link to policy is different - it’s overwhelmingly supported and not even generally classed as a political view anymore (along with “is evil bad?”).