The word "they" is a little broad. If "they" means the wacko far right fringe who carry or are carried by the religious far right, then yes, it is a fact that they will not stop. But then, that's all it takes to create a monster that can cause a lot of ugly, just the fringe. The less fringe religious right are less of a direct problem but just as much to blame because they will allow it.
My apologies to the religious people who support freedom and civil rights but I still have to say that I believe religion poisons everything.