I know Harkins (a southwest chain) allows outside food so long as it is non-disruptive, non-alcoholic, and they do not sell it. You can't bring your own popcorn or M&Ms or soda, but if you wanted to bring in tea or a coffee from one of the Starbucks in the strip mall or even McDonald's, they're generally A-okay with it. I've seen people ask about it numerous times and they are always allowed to bring it in.
They just want you to purchase their food but seem to realize that every piece of food brought in is not a lost sale, unless that food is something they already sell themselves. Which, in my mind at least, seems reasonable.