only government can infringe on Constitutional rights. that said, 2A says nothing about location, public or private property. so private property rights are at odds with 2A rights, or so it would appear.
private property owners have a right to choose - is actually not accurate. My Constitutional rights do not end when I am on someone else's private property. the owner can ask me to leave, or trespass me, but they can't deny my Constitutional rights on their property. Same if I exercise my 1A rights on their property.
that local bar owner that banned guns in her bar, I respected her choice, but my 2A rights are not void because I am on her property. If I wanted to push the issue, I could go to her bar armed. she can't deny my Constitutional rights; my Constitutional rights don't end because I am on her property. her attempt to deny my Constitutional rights is just that.
I choose not to go where my 2A right is infringed or denied, public or private. However in the case of private property, I have no obligation to surrender my Constitutional rights.
To differentiate, private property owners can attempt to deny my Constitutional rights, I have no right to be on their property but if I am on their property they can't deny my Constitutional rights, all they can do is ask me to leave or trespass me if I refuse. The police won't arrest me for exercising my 2A rights, only for trespass.
whereas on public (government) property, it is indeed an infringement of my 2A right if the government denies that right on public property.
while only government can infringe on Constitutional rights; private property owners can deny my Constitutional rights but I am under no obligation to surrender my Constitutional rights because I am on their private property.