AMC may not be supportive of it, but I use mine at my local AMC theater all the time. You check in with the app, go to the counter then use it like any other MasterCard. Unless the theater specifically tells employees to look at people's cards and then tell them they won't accept a MoviePass branded Mastercard, I don't see how they can prevent it.
I would guess that refusing a specific legitimate MasterCard would violate their merchant agreement and tehy probably don't want to mess with masterCard. If they are so worried about MoviePass devaluing the movie experience then use the added attendance to show people that going to a movie can be worthwhile so tehy comeback when MoviePass goes bust. Use this as away to build some interest while you take MoviePass' money.
If I were at AMC I'd tray to track the added revenue from MoviePass in terms of concessions, etc bu getting people to link the AMC rewards to their MoviePass card, and then see if the added marginal revenue makes it worthwhile to cut a deal with MoviePass to keep people coming more often.
I can studios being worried if it cuts into the box office and thus their revenue and blockbuster box office PR.