Satire doesn’t require falsehood or exaggeration.

In this case, the two parts of that statement (“My religion is opposed to jacking off”, “I don’t care about feeding the poor”) aren’t usually made explicit or said together. By saying the quiet parts out loud and putting them in direct juxtaposition, this headline calls him out on his hypocrisy.

Yep, this is accurate if it weren’t written as a quote. Since it is it’s satire but, as with all great satire, based in fact.

What you’re referring to is parody. Satire is exactly like this.