Admission into a place that is open to the public is different than baking a gay wedding cake. Baking a cake requires something to be done -- it is active. Admission to a place is passive.
It sounds good in theory, to
"let the public decide whether these businesses continue to operate by means of dollars"
but the reality is boycotts don't work. Look at the states (mostly in the southeast) that have binding signage; I have not seen very many restaurants or retail stores go out of business because they put up no guns allowed signs. People either ignore the signs or leave guns in cars. Neither is a good idea. Your gun is safer on your person.
Look at Disney, (and Florida does not have a binding signage law) they banned guns for years even though the Reedy Creek Improvement District (which controlled all disney land) was a local unit of government with its own fire dept and LE authority that was contracted to the Orange County Sheriff.
Gov. DeSantis targets Reedy Creek. 10 things to know about the Disney-run tax district
Reedy Creek: The Facts You Need in 2024 - Disney in Florida
No one cared until they disagreed with the despotic Gov. DeSantis on homo sexual education it was only then that he clamped down on Disney's special exceptions in Florida law and changes were made. Gun owners went to Disney and left guns in cars -- not nearly enough people cared to make a difference. And Florida politicians even one who claimed to support second amendment rights ignored the blatent violation of the pre emption law by a unit of government.