The only Fluxx sets with significant goal & keeper overlap are Fluxx and Family Fluxx; certain keepers are duplicated. Those two can be mixed, and mixing those two isn't a clear "Should not"... but the others, they definitely fall into "should not."
Such mixing definitely lengthens the game, as needed keepers are harder to acquire. It also reduces the skill factor and increases the luck factor of victory.
If, however, you simply want to mix the new rule cards and action cards, playing with only one set's goals and keepers, that does work somewhat better. It still potentially lengthens the game. (See note.)
Note: I say potentially, as the shortest game I've ever played was a combined Fluxx/Family Fluxx game. First goal was runny chocolate, I had sun and several other keepers, and the 1st player played "Play all"... and played a chocolate. I drew, got "Steal a keeper", stole his chocolate, and played my sun, thus filling the goal, and winning, 2 minutes into the game.