Fred Phelps thinks that God hates fags, right? He's got all kinds of little add-ons to that theory, but basically his whole life's work boils down to fag hatred. So if they make signs that say, "God hates mopeds," they are mocking his message.
Pretend you're Fred Phelps. You see that sign. How does that make you feel? THOSE PEOPLE ARE MOCKING ME! THEY SHOULD NOT BE MOCKING MY MESSAGE! I AM TRYING TO SAVE THEM FROM THE WRATH OF GOD BY SPREADING MY MESSAGE!
See, that's what Fred Phelps would probably think because he's a complete idiot. Mocking idiots is funny. Do you get it now?
If I have completely misinterpreted this joke, someone please correct my egregious error. This is just how I interpreted it.