Would you be okay with your SO talking to their ex?

So my boyfriend has been talking to his ex a lot recently and I’ve told him I don’t like when they talk but he still does it anyway. He says they don’t have any feelings for each other or talk about anything bad and it’s just a mature friendship. I want to trust him but I can’t because of the fact that he hides to talk to her and he deletes the messages between them. He tried to call her yesterday before coming back home and didn’t tell me anything. IMO if it was just plain talk he wouldn’t have to be hiding or deleting messages. Also, I don’t like that they talk because many times she’s given the impression that she’s still into him and wants to be with him. For example, when we were having problems, he went for her to advice and she told him to leave me. Before that she told him she wanted to have his babies. Recently, when he told her I moved in to live with him, she replied in a way that gave the impression that she was sad about that. I’ve already tried talking to him about it and I told him how I felt about it but he literally defended her and said he’s not going to stop talking to her just because I don’t like her. Before I moved in with him he got mad at me because I was talking to a guy friend so to avoid any problems I stopped talking to everyone and only talk to my best friend. I don’t understand why he can’t stop talking to her knowing that it bothers me and still expects me to not talk to anyone else he doesn’t approve of. I guess I would tolerate it if none of that happened and if it was really just small talk and he didn’t hide to talk to her but after all of that I don’t really trust that it’s just small talk. What would you do in this situation?