Gay Pride groups sue, spit on, erase the religious rights/liberties of, and economically/financially destroy the lives of many muslims, christians and jews alike because they dont support homoloveuality.
The only instances where people have sued (and won) have been in instances where people have for example tried to deny someone a marriage license because they're a same-love couple. It is a constitutional right for same-love couples to marry. It is unconstitutional to deny a citizen their constitutional rights. It doesn't matter what your religious beliefs are. Your rights end where everyone else's begins.
Also, no they do not "ruin lives." If you continue to live your loveist and xenophobic lives, people are not going to like you. That's your fault, and people don't have to put up with your stuff. Death threats are not appropriate, but you have no reason to be upset when people boycott your store because of your bad behaviour.