As JWL pointed out "fair use" is a critical concept here. While it allows some bending of the rules, it almost never applies to any sort of public performance. If the event isn't publicized and its open to a small group it
might be legal under fair use. However showing part or all of a film in any sort of public performance is almost always illegal without permission and royalties.
The truth. You probably won't get in trouble as a theater and you personally probably will be the last one to get in trouble if you get caught. They will probably go after whoever runs the theater.
My suggestion. Do some more research about what the penalties are for doing what you are being told to do and what it would cost to do it legally. Then write an e-mail to your boss saying, "I'm really uncomfortable with what is going on. These are the potential consequences... this is what it would take to do it legally..." Be informative, not disrespectful or confrontational. Suggest that you take a look at establishing a theater policy about copyright law. Do your job and keep
track of the copy of the letter in your outgoing e-mail box in case you get busted. So you can say, "I tried to tell you not to do it."
If you don't get any positive response, bring it up again a few months after the event is over (perhaps even going over your bosses head). However this time bring up the need for a policy generally when a specific show isn't on the
line. Push whoever your upper management is to make a policy that everyone will have to follow. This sort of thing happens far too often and to me isn't worth getting fired over so be informative not confrontational. Research and show them the potential consequences vs. the costs of doing it right. "They"
are out there looking for rule breakers and they
do bust theaters so for the long term good of whomever pays the bills it is a very wise thing to have a strict policy and follow it.
Also if you are going to post openly questions like this, it might be a good idea to not include the exact name and location of where you work in your signature.