if we didn't allow these frivolous lawsuits then that would block legitimate civil suits too, what we need is a way to discourage frivolous lawsuits like some states that require the plaintiff in civil suits to pay all legal expenses of the defendant if the plaintiff loses the court case.
But what I'm not buying is the idea that if a company simply leaves "weapons" out of their workplace policy that it would have any effect of them being sued implying they 'allowed' their employees to carry guns... there is also a good chance that Uhaul can be sued here regardless of a gun free policy. Policies can be written to explain prohibited behaviors like threatening, dangerous, illegal and intimidating behavior and leave it at that and would be plenty to still fire someone who doesn't know what concealed means.
That's what I'm talking about. My old Dad told me "Any one can sue anyone for any thing". You may not win, but you can do it. The problem is too many stupid law suits get ruled for the plaintiff. And too much money is awarded for a lot of them. I think that having the no fire arms clause will help limit liability. My main point though, is that it's not so much a left/right thing.