You own your opinions on said thing, yes. Having an opinion on something is one thing, that's always going to happen. That's why publishing requires some thick skin. Everyone is going to have a different view on your work and some might hate it.

But you will never own the characters, not ever. Not yours.
An author is perfectly within their rights to tell you: not in my sandbox, no you don't, not allowed. They can tell you, no Fan-Fiction, please. And they are well within their rights.