No one has any rights that trump the owner's right to set his own conditions for dealing with the public. If you won't disarm yourself before entering then you have the choice not to enter. Nothing else is morally acceptable.
I can honestly understand your position but it does seem that there are a number of states who's laws don't exactly see it that way by giving the gun owner a chance to exit before charging him or her with a trespassing or more severe count.
They don't make it an immediate criminal offense like Tennessee does.
Those states have granted the "legal" privilege to carry a gun and it appears that they feel that privilege over-rides a sign to a partial degree. If the gun carrier does not respect the owner's requests and leave, it is then and only then that problems could arise.
Yes, you could choose not to enter but at times that choice is extremely impractical and your sense of moral acceptability may have to be over-ridden.
For example, if you are with a group of people and you are the driver. You park the car at a considerable distance and the group decides to eat or go to a show that has a sign on the door. Your gun is fully concealed and no one knows you have it. What then do you do? Me, I would enter and stay with the group and not feel one bit of guilt about it.
OTOH, if in a condition of open carry, I would not enter because I would obviously antagonizing a situation.
A real problem develops in a state like Virginia where you must open carry in a place that serves alcohol to stay within the limits of the law. If that establishment is signed, then under the condition described above, your only choice, to stay within the law, is not to enter no matter how many people you have with you.
It really boils down to a matter of choices but the one thing that bothers me is that an establishment that posts a sign is probably not responsible for my safety if I left my gun in the car and something went down while I was in there.