Is this an ongoing thing or is she new to this? I've heard this as an initial reaction when being introduced to polyamory, and it changing with a little encouragement. For me, personally, it would be a dealbreaker. I don't live half lives or double lives. It's all inclusive.
This is the woman who you don't trust to use condoms, so I can see why you are skeptical about her in general. Usually, just the fact that she doesn't want to be friends is not a red flag in and of itself, but I sense from the tone of your other posts that you have a bad gut feeling about this. It sounds like you want to do what's right and you have some reason(s) why you don't trust her. Not wanting to at least meet you, and you wondering about it, tells me that there is more to this than what is visible on the surface.
She has been with married men before, but in secret. Their wives have known nothing about her... One of the men she is seeing is married, but his wife doesn't know. She is new to the wife knowing aspect of it, doesn't see the point, or believe that we need to be friends, or even know each other. I don't know if I should just step back and see how things play out, or stand my ground.
I'm a little curious if your husband isn't seriously concerned about this woman's chronic dishonesty in relationships.
Are you okay with your husband having a double life that excludes you?
Why is he choosing to be involved with someone who isn't interested enough in his life to even meet his wife, and who seems to have a preference for dishonest relationships?
I would definitely suggest taking every precaution to make yourself sexually safe with this woman in his/your life.
I told him at dinner tonight that i am seriously thinking about going back to using protection with him every time. I am that scared or paranoid, or however you want to see it.
Personally, I don't need my partners or partners' partners to be best friends. It would be lovely, don't get me wrong, but I think that expectation is unrealistic. Having said that, I need people to be able to meet and be civil to each other. If they can't manage that, that is a dealbreaker for me. I wouldn't be happy in a situation where my partner's partner did not want to meet me or get to know me.
It sounds like you have a really bad vibe off this woman, and part of me is wondering why your partner isn't listening to your concerns. The information you have given so far about this woman suggests you don't trust her to be respectful of your relationship, and that would raise alarm bells for me.