This is 100% not the case with real shops, you cannot be thrown out simply because the owner wants to.
It's also still not right.
It's also still not right.
> It's also still not right.
No, it is not right, but just like a shop-owner, a forum moderator will not ban you randomly because she has an interest running a popular forum.
If one gets banned from a community(online or not), in most cases it's because they didn't adhere to the written or unwritten laws of the community, or pissed off someone high in the pecking order. Communities are not democracies, but my guess is that even if they were, a big majority of those who get banned would be ostracized anyway.
Political opinions, skin color, sexual orientation, what they had for breakfast?