The fact that I'm critiquing a poor argument has nothing to do with my philosophical views. Just as I could argue a fascist policy would be poor to implement or is inconsistent (or the opposite), I can do the same with liberal democratic property rights.
While a view may not be property (and this depends on what laws are written etc...) communities in this system of government regularly create laws and regulations for said communities. It's just a normal thing that happens in democratic societies. Being upset about that doesn't change that fact, nor does it make those communities immoral or unethical or anything like that.
No you're not. You believe in private property in views.