What veterans fought (fight) for is freedom. Freedom includes being able to deny access to private property for any reason not specifically part of a "protected class".
I hate that argument. It implies that private vs public property is binary, that if some land or property isn't literally owned by the public then the owners should have the same power over visitors whether it's a private domicile, or an open undeveloped field (on private land), or a typical open-to-the-public store, or something in-between like the American Legion or Sam's Club.
I don't think that's the right way to look at the question of private property rights. I think even membership-only clubs shouldn't have unilateral power to prohibit responsible concealed firearm carry, any more than they should be able to dictate what color underwear should be.