I still remember the huge sentiment during the Obama years of "he is still our president and you should respect that."

This is an older principle that is no longer adhered to. I'm sure someone did try to bring it back for Obama, but that's not a cat that's going back in the bag easily. SNL parodies the presidents, and they're as mainstream as it comes.

That said, respect for the office does not mean that you don't criticize its occupant or even make fun of them. That always happens unless some gestapo cracks down on it.