Religion is known for encouraging discrimination and violence against LGBT people - isolation, being looked down upon, rejection, disowning, torturing and the death penalty. LGBT people are harmless in their protest against religion, they still allow others to practice it and don't encourage discrimination or violence against them.
Because of the history religion has against LGBT people, it's a lot more offensive for someone religious to hate on a LGBT person than vice versa because the religious person is seen as being associated with or endorsing its known links to previous and current discrimination and violence, where as an LGBT person will be seen as fighting for their freedom - and to be fair, that is all they are doing