Since the conservative movement as a whole has been generally moving to deny LGBTQ people the right to marry (see: attempts to overturn Obergefell in conservative states), the right to serve in the military (see: transgender military ban) and the right to not be discriminated against (see: masterpiece cakeshop).
I'm not going to deny that there are LGBT conservatives. But the fact is that conservative politicians as a whole demonize LGBTQ people and have attempted multiple times to censor them [1] or bar them from aid.