Their philosophy is extremely inconsistent. In reality it's emotionally driven. Not sure what specific emotions cause one to think sex is wrong except for reproduction, but a lot of the people who push this sort of thing turn out to be closeted gay homophobes.

I’m not supporting it, but how is it inconsistent?

I can speak more to the Catholic view than the evangelical, but if you accept the initial premise that there is a creator God then the rest follows fairly naturally (you can look the ‘the theology of the body’ if you want to read more)