I want my partners to care, but I'd be worried if they had only negative feelings about it. I'd want them to have mostly or only positive feelings about it.
I'm glad to have a boyfriend who can protect me if I need to be protected. But he would never do it without my asking for help. Otherwise if someone is flirting he assumed I'm fine with it (unlike some other guys who would assume he's bothering me).
I like having someone who protects me, but I would think it condescending if they assumed they know better than I do what's good for me. So letting me make my decisions and respecting them is very important to me. This being said, I take my boyfriend's opinion into account and would want him to tell me if he's got a bad feeling about someone.