Boyfriend (M56) is friends with ex wife (F55) on Facebook

My boyfriend, for 2 years was married for over 30 years, divorced for 4 years. His ex cheated on him several times and he has no respect for her. They have 2 adult kids together (31 and 26). I'm a 55F, secure in my relationship with him, however, he refuses to unfriend her on Facebook. She barely commented on his Facebook posts until he started tagging me on his posts, then she's commenting or liking the posts. It really irritates me because they show up on my feed and my friends have commented on it. He doesn't want to unfriend her because they do have kids together and he wants to see any posts she has that relate to the kids (I know, if she tags the ADULT kids, he will see it). I feel like he's using that as an excuse to keep track of her. I have an ex husband as well, but no kids and we are not friends on Facebook. Would you give him an ultimatum to delete her on Facebook or just ignore her comments and likes? I feel like she's just trying to stay relevant in his life.