Even with the current President speaking, the show was never what I would call "political." In fact, my favorite of the modern versions featured a guy I never would've voted for. The problem is
anything historical comes with political baggage these days. E.g. I've seen criticism that Andrew Jackson basically gets a fluff piece in the current version,.
That said, while I agree it's time to retire the show, I think we need a clean break. Something absolutely unconnected to politics and politicians. Otherwise I think the optics will be horrible. Also, the Muppets are a dinosaur IP outside Disney fan circles, and musical-comedy A-A shows do not age well ("Veggie veggie, fruit fruit", "It's fun to be free..."). I'd almost rather they go with
@GAcoaster's idea of Mr Lincoln East for the time-being, let guests take air-conditioned naps, and go with a complete rethink once money opens up. And yeah, Sleepy Hollow would be my vote.