Opposition to the stigmatization of minority human beings is not bigotry. It’s a moral necessity.
The Roman Catholic Church teaches that LGBTQ people — minority human beings — are depraved and disordered.
Those teachings are evil and horrifying in precisely the same way Nazi and KKK teachings are evil and horrifying.
Opposing the leadership of evil fascists and racists is a positive moral requirement for any human being who considers themselves to be decent and moral.
Opposing the leadership of evil homophobes is the same requirement.
No bigotry involved.