I'm curious about how much dropping in and out would be acceptable during a coop run. Some skips simply aren't possible with two players because of the lack of split screen (thinking specifically of the skip to get into the sandcrawler in 4-2.) Is it legal for one player to drop out so the other player can do the skip and then immediately drop back in? Or is it necessary for both players to remain dropped in at all times, barring the crazy circumstances the lack of splitscreen likes to cause?

I feel like it's a completely valid tactic, and is a use of the games mechanics, which is what speedrunning is about isn't it? Using and abusing anything given to you, intentional or not.

Personally I agree with you, since it is an intended mechanic of the game. My worry is more about the definition of the category. How much of the run needs to be done with two people for it to be considered coop? There are skips that are possible in single player but not in coop because of the rubber banding if you get too far from your partner. Are those skips legal, or do you have to forgo them because it requires using only one player and thus (in some way) violates the definition of the category?

I would say that you would have to most of the time be in co-op mode, however a player can drop out so that a skip may be performed. Once the skip is performed, the second player must rejoin the game.