It is a dilemma, to be sure.
If you let it be, or are inescapably, intrinsically compelled by this opinion, then yes. Otherwise, no dilemma at all. I've never been able to grasp, understand, or accept how there is a "right" to not have someone else do or possess something in your presence that you have no knowledge of and/or which you suffer no harm from. This might as well be a right to have people not believe something or think something or mumble something under their breath that you don't like. Or not pass gas on your property, or wear purple underwear. This is such an ephemeral concept of a "right" as to have utterly no meaning at all.
If we don't carry when asked not to by those who prefer that nobody be carrying a gun, even though we all know criminals don't obey laws or respect rights, we are respecting those folks' rights.
When pushed to accept such an ephemeral and merit-less concept of a "right" I will freely state that some RIGHTS absolutely take precedence over other "rights." Your RIGHT to self-defense wins over my "right" to (not even sure exactly how to phrase it) ... not be in the presence of some object I have no knowledge about or contact with.
If we carry anyway, we're doing what we think is justifiable even though it is also, no matter how you slice it, going against the rights of those who desire to create and enjoy an environment where there are no guns.
But there is no reality in this created environment. It is meaningless and vapid, unless they're enforcing that "right" via metal detectors and running around naked inside a walled compound, they have no real hold on the reality they're claiming to try to create. For their pragmatic purposes, me coming in with 37 guns secreted about my person is just as good as me entering disarmed. The benefit they receive from the enjoyment of their utopia is not lessened by my presence.
From the perspective of individual rights, it is beside the point that crooks will have guns no matter what the law says and no matter how the policy of the property owner reads.
From the perspective of the restricting individual's claimed "rights" ...ok. From the perspective of my right to self-preservation,
"He who goes unarmed in paradise had better make darned sure that's really where he is."
It's quite ironic to me that some of us see these place as so desirable that we are willing to commit a property rights violation in order to patronize them, and yet so dangerous that we won't disarm before we enter.
And so dangerous? Tell me again about all the "safe" places in this world where we can go and know that we're secure from harm. Now recall that we're talking about bars and restaurants and let's juxtapose those notions.
As I said, this theory doesn't pass the sniff test, for me.