Yes, but only one side can say "because climate change exists and is very important, you should do X".

The other side would have to say "because there is no climate change or it isn't very important, you shouldn't do X if you're doing it because of climate change". That's fundamentally less convenient politically because telling someone "you don't need to do X, at least not for this reason" is a much weaker sort of demand than "do X", even though in some sense both involve demanding that people do what you want.