I have not read Hoppe, so as someone who has perhaps you could help me understand some things.

"It is therefore not controversial at all to say that a property owner has every right to exclude anyone from his/her property, for any reason, at any time."

This is true although it doesn't necessarily make it moral. I have every right to be dishonest (provided I'm not defrauding people of money or property), that doesn't make it moral to tell a lie just because I can.

Likewise I can exclude people from services based on purely arbitrary reasons like race or sexual preference. That is well within my rights but doesn't mean I'm not an arsehole for doing so.

"...and the conclusion is that the alleged enemies of private property preservation “will have to be physically separated and removed from society”, so to speak."

Without a government (which you've clarified) I could only envision this actually happening if everyone in society unanimously agreed to exclude someone from their private property. I could see that maybe happening to someone who is an infamous thief of fraud, but if they're only doing it because of differences of opinion, I just don't see how society would unanimously agree to do that.

Say there are ten supermarkets in the suburb where a communist lives. How is it conceivable that all ten supermarkets would even know who he is, and even if the did, how would it be conceivable that all ten supermarkets by some coincidence decide to exclude him based on his preference for communism? Or what are the chances that all the business owners/share holders even care about his preferences?