When is it appropriate to stay in contact with an ex lover? Generally there seems to be three reasons people stay in contact with an ex: 1) you genuinely want to be friends with them, 2) you use them for backup attention/self validation/hookup, or 3) you want to restart a relationship with them. 1 and 3 are acceptable, 2 is a bit selfish but understandable and can be perfectly alright if the other person is also using you for 2.
Where there are issues is when you and the ex mismatch on what you want. Admittedly I don’t think I’ve ever mutually wanted to stay a friend with an ex. So I’m not. The worst case is when one person is a 3 and the other is a 2, that’s when people can get hurt. As long as everyone stays honest, then you should be in the clear, but it’s hard to be honest, especially with yourself.
Now if you are trying to move on and date someone else, then I think the only case that works is if you are both genuinely in 2 space. If you are still interested in the other ex, either for 1 or 3, then you should break contact off with them if you are actually being sincere to the person you are currently with. I just recently went through this logic.