There's definitely room for criticism, though also for justification.
The sentence has two clauses. The first is straight forward, and could stand as an independent clause. Indeed, as an independent statement:
Do not be the person we ask to leave the auditorium
The second only makes sense in the context of that previous clause:
On it's own, that's meaningless, but in context "we will" refers to the action that "we" have mentioned doing. So to re-write it as a fully independent statement, it is:
We will ask people to leave the auditorium, if they are texting.
Of course, that clause is entailed in the first one. It's stated because people might not believe the rule is actually enforced. So we could re-write it again as:
We really will ask people to leave the auditorium, if they are texting.
So, two fine clauses, with a sensible relationship to each other, how to stick them together? Generally there are three options:
Put one after the other as separate sentences:
Do not be the person we ask to leave the auditorium. We will.
Put one after the other with a comma, semicolon, colon, or perhaps a dash:
Do not be the person we ask to leave the auditorium: we will.
Or we can join them with a conjunction. But what conjunction to use? The choice of conjunction reflects the relationship between the two clauses. In this case, the relationship is that the first clause states a situation that you should avoid, and the second that the situation can indeed happen.
Some near-synonyms with overlapping meanings that are likely suspects here are because, as, since and for.
Of these, because can be justified, or condemned. It can be justified: we can interpret it as saying we should avoid being thrown out, and we should do so because the rules with that penalty are being enforced.
On the other hand, there's a disadvantage with it; they spend so long talking about the reasons why texting during a movie isn't a nice thing to do, and then they say the reason you shouldn't do so is that you'll be thrown out. Really, the reason not to text in the the cinema is not to be a bloody nuisance, and the penalty is there to be a disincentive to people who are bloody nuisances anyway. So if you want to include it as a reason, but not the reason, you might favour the conjunction for. And that is presumably what they mean.
But then again, if you aren't that much of a stickler about using because as precisely as that, then you won't care. And since for as a conjunction has a rather formal tone, it makes sense to go for a slightly questionable use of a common conjunction than one that changes the tone from that intended.