A couple of thoughts:

There is a concept called "higher law," which states that some rights trump man made laws. It's recognized in our system, English Common Law and Hindi law among others. The right to defend yourself and your family is one of those higher laws.

The your lawn or home analogy is completely off base, you do not live in you sub shop, it does not have the same legal standing in many jurisdictions as your actual home.

I rarely, if ever go into someplace where no carry signs are posted, however, I'm sure all of the dead in Colorado wish someone had been able to defend them. Gun free zones simply do not work and endanger the public. In the end, your right to be an anti-gun loon does not trump the public's right to protect themselves. I do not see where this even deserves debate.

Most of the above I addressed from a principle/theory standpoint. That said, I agree with most on here, the polite thing to do is go to a similar business that does allow CCW and respect the sign if at all possible. Why create strife if you can avoid it?