Is there such a thing as an under-protective boyfriend?

My bf was over and my ex dropped by the house, which he almost never did, and he mentioned his car, which got my bf talking about NASA and they hit it off! And now he's best buds with him even though my

ex cheated on me twice. My ex flirts with me right in front of him but he doesn't seem to care. I visited him and my ex was at his house and they were watching sports together with a few other friends.
I mean, I don't want them to fight but it's just awkward that they're always hanging out together.
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I wasn't sure if I should put this into dating, family and friends, or breakup and divorce. So I just went with this.
Is there such a thing as an under-protective boyfriend?
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