The evangelicals believe that anyone who doesn't believe in their god will be tortured by their god for eternity. There's nothing worse than eternal torture, so they see it as their moral obligation to do anything at all to prevent others from being tortured for eternity by their god. Nothing they do to others can possibly be worse than that, so as long as they're focused on saving others any actions they take are justified (to them).

Their god considers gay sex a crime worthy of eternal torture. So anything they do to prevent people from having homosexual encounters is morally acceptable, up to and including torture & occasional execution via "conversion therapy".

Anyone who truly believes in hell is either morally bankrupt & willing to allow others to suffer for eternity, or a dangerous monster who will stop at nothing to prevent others from what they see as sinning.

Many of them don't go to the extremes they would if they actually believed they were saving others from hell. They're full of shit. But some of them do, and they're fucking terrifying.