Banned places in MA:
Schools - MGL 269-10j
On the surface of the ocean within 500 ft of Logan airport -- MGL 90-61
Where birds or mammals may be found if > 38 caliber (hunting regulation, and no, people are not mammals under the definition)
Logan airport outside the sterile area (CMR, $50 fine, does not apply to transport for travel)
Anywhere while you are under the influence of alcohol
Many state buildings and courthouses by administrative fiat, not law (court order in the case of courthouses)
Plus the assortment of federally banned places (airport sterile areas, federal buildings)
And, actually, the "the most they could do" is report the attempt to ignore the sign to the issuing PD asking that your suitability be reconsidered. This is not likely to happen if a store clerk sees your gun and you leave, but could be an issue if you attempt to sneak a gun in past a private sector security checkpoint with detail cops present.
Since the MA carry permit law pre-dates the widespread carry permit movement that started with FL, and was only originally intended to prevent "undesireables" from carrying, it is not littered with the carveouts, banned areas and binding signage found it some other state's laws.