Talk about "strawman" , holding services & handing out pamphlets are actions, and often talking to folks not interested; akin to handing out guns maybe?Tell me–does a business have the right to tell someone they may not hold religious services on their property? How about hand out religious or political pamphlets?
Or is that violating their 1A rights?
The first only denies Congress the right to establish a religion, doesn't protect pamphlets (not that I can find) it does protect free speech however.
A better example would be can someone in a store say "God bless you " when someone sneezes , or "God go with you" , or "God bless" when checking out etc. carrying arms is not "in your face" (though some try to say it is, it's not) LEO do it all the time and who pays attention? Oh yeah , lately thugs have been trying to make that an issue , even killing them on the job.
Academic exercise anyway, since I've never seen a "no religious pamphlets " sign, much less someone getting arrested over the sign like you can in some states for crossing a no guns sign (that is the BOR issue & violation btw signs having the FOL involving agents of the state- LEO) even IF you really didn't see the sign.
Regardless, carrying of arms in public is protected outright