Who is to say that the 2nd amendment right trumps private property rights? You are saying in essence that if I post my property "no guns allowed" or "no fishing" or "no whatever" that you have the right to ignore my rights.

And that ain't right

I would not equate a no fishing sign to a no guns allowed sign. Fishing isn't recognized in the US Constitution. I'm also not espousing that a ccw holder disregard a "No Guns Allowed" sign. I believe as stated by previous posters that I just would not patronize those establishments. In reality though if cc was done right how would you know anyone was disregarding the sign?
Although a restaurant,movie theater or retail store is privately owned it is dependent on public patronage to exist so I'm not sold on the no tresspassing or fishing comparison.