Can Monty Python Fluxx be used with the regular Fluxx deck, or is it a separate game?
You certainly can just shuffle the decks together, try to play a game with them, and see what happens.  The core rules of Fluxx are always pretty much the same, after all.

However, everything I've heard from people who've tried something like this suggests that, for maximum enjoyment, you'll probably want to start removing cards that don't work well in the combined game; or adding your own homebrew cards that will work well in the new game.

I'm not very familiar with Monty Python Fluxx, but I've played a bit of Zombie Fluxx - and it's pretty well optimised on its own.  I could add my basic Fluxx game into the mix, but then the zombie theme would be much diluted.  It would be much harder to assemble a critical mass of zombie cards to achieve one of the zombie Goals - or indeed the non-zombie cards required for a base set goal.

But in the end Fluxx is a game that it's best not too take too seriously.  If all you're after is a nice long, random game with the possibility of unexpected interactions between cards from different sets, then I don't see why you wouldn't want to at least give a mega-game using cards from multiple expansions a try!