Pretty much, Your position is that I follow your rules on your property, In the context of "Private property" I think that is simple courtesy. Where we differ is in the matter of "Publicly accessed" private property such as a store or employer.
You say "private property is private property, you don't have to go there.
I argue that if you wish to use the services, or take the job you do have to be there somewhat involuntarily.
Just like you can not deny service to someone for being a Jew.
Whether or not to practice a religion, and your choices in the matter, are purely voluntary and are protected by the 1st Amend. You can not be discriminated against on that basis. It's why people are so PO'd at the Muslims, they are using our own laws against us.
Whether or not to carry a firearm, and your choices in the matter, are also, purely voluntary and are becoming more protected.