The real problem I have with Christian Fundamentalists, is that any mention of the LGBT community that isn't condemnatory, is seen as "promoting" it. DJS is correct that studies have shown conversion therapy to be a failure, with many individuals being psychologically harmed from the attempt to change their orientation.
The political agenda of the LGBT groups is little different from that of the Civil Rights movement. All of us are equal, and deserve the same rights and freedoms, no more or less than anyone else.
Of course there are always those in whom Political Correctness preempts common sense(the reaction to the teacher's remark in British Columbia was ludicrous). However, in the case of Prof. Peterson, I don't see how asking you to be sensitive to someone's preferences in gender-neutral pronouns is an infringement of your free speech rights. Being a male, I would prefer not to be called Miss or Mrs. Many transgender or gender-neutral people would simply like to be addressed by the terms they associate with themselves. No big deal.
Anyway, as DJS also said, If certain Christian groups didn't have this irrational fear of sexual orientation, this problem wouldn't exist. We'd all be much happier.