On your property I agree, but this is a weird case where by denying carry on your property (and we're talking business property that is open to the public, I wouldn't carry on your farm or in your house if you didn't want) can deny me the ability to exercise my rights while not on your property.
Of course I can choose to not go there and in my case were it a single place I walk to eat I'd choose another place, but that's tougher if it's a college where you go to school or some other more necessary place like the only grocery in the area, etc.
It's also complicated by the modern reality that we have deemed public businesses as only quasi-private. I'm not defending that decision, again it has good and bad sides, but we have determined that no business can refuse service on basis of race, creed, religion etc. We've decided those things are important enough to breach property rights for public businesses. Of course on your own private non-business property you can do as you choose.
IMO if we accept that infringement for something we believe is the right thing, even though non-discrimination isn't spelled out Constitutionally, it seems reasonable that Constitutional rights should also be so treated within reason. Free speech isn't prohibited explicitly on property but falls under trespass and I'm fine with this doing the same.
Even with all that, if it weren't for the impact no-carry decisions have off the property in question I'd still probably support it being a business/property owner decision, but the logistics of carry mean they can have an impact beyond their property rights.
Like I said, I'm torn both ways. I see lots of gray and no wrong answers. All of us are wanting to protect our basic rights and I support anyone trying to do that even if we disagree on the balance.
I completely understand.
And for the record, while I disapprove of anyone denying service in a business on the basis of race, religion, etc (I firmly believe it is wrong to do so), I completely disagree with the laws prohibiting such. To me, property owner's rights on their property is paramount to anyone else on their property. And if Big Al's butcher doesn't want to serve to (insert race/creed/color of skin here) because he's a bigot, then he should be able to not serve them. Doesn't matter how I feel about it because it's not my property.
Here in Colorado, we recently passed laws that added the gay community to those who cannot be refused service. Except that this law, IMO, goes way too far.
I can walk into a local gym, and walk right into the women's locker room, and go shower in their shower. All I have to do is say that I'm gay, or that I'm really a woman trapped in a man's body, and there's nothing anyone can do about it.
So here we have a law, in the name of "tolerance" (which it's anything but to anyone who isn't part of the agenda) that could literally force some businesses out of business. Some pervert could go into the women's locker room at a gym every day, and make the people in there so uncomfortable that they stop going to the business, all because he "identifies more with being a woman than with being a man". And there isn't a thing the business owner can do about it.
Now, If I were a business owner, in my business, anyone is welcome. Regardless of skin color, religion, sexual preference, especially gun people. But if you have predjudices and don't want to allow a certain group into your business, I firmly believe you should be allowed to deny them service at the expense of losing business.