The first option could lead to easier theft of the gun, putting guns into the wrong hands; it also means bars have to be responsible for something they may not want to deal with for moral or political (i.e., PR) grounds; the second amounts to a stigmatization of gun owners in the form of an undue burden upon them and no one else.

Make what you will of those arguments, but note both options could also be applied to car keys of people entering a bar (check your keys so we can evaluate your intoxication before giving them back). In fact, one could note that cars are a tool much much more often used by the intoxicated to murder (commit manslaughter, if you like).