My state has made it lawful for me to carry concealed, with exceptions.
A business with a sign is not an exception under the law.
Period.
If management chooses to engage patrons and challenge every bulge, it will end badly for them (go woke, go broke).
If asked to leave, the law stipulates that refusing is trespassing and THAT is the only exception which will apply beyond the CHL statute.
After that, it's game-on (civil proceedings against them).
FRiendly advice: GO right (don't lean).
I’m a big believer in the 2A. But I’m also a big believer in property rights. So if a business posts a sign, I will either obey that sign or shop elsewhere.
I believe that’s a reasonable, conservative position. Of course, your mileage may vary.