Dom/sub/slave in public?

I saw this on Facebook and thought it would be a good conversation starter. For those of you who don't know, an uncommon kink is having a "slave". It's a subset of BDSM and the dom/sub dynamic. The slave can be compensated via sexual favors but often is just treated like the family pet. They cook, clean, and even go as far as acting like footstools. It's 1000% consensual and again, not always directly sexual in nature. I saw this post with the pictures showing two people practicing this kink publicly. Do you think this should be allowed in stores and other public places? Or do you think that we should allow it because it's not really sexual or showing anything inappropriate? Thoughts?

Also to add, these slaves don't act like animals. They act like humans. But are incredibly submissive. And often don't get human like privileges.