Of course you are not wrong to be concerned about your boyfriend staying friends with his ex. Your needs are very important in this and if your boyfriend is turning a deaf ear to your feelings then you will inevitably begin to resent him.
It is all too easy for people like your boyfriend to take the line "we are just good friends now" or "you are so possessive and insecure".
The reality is that your boyfriend probably feels like less of a "bad guy" for leaving and upsetting his ex. Does he worry about pleasing people?
For all of us, letting go of someone is painful, even if it is our choice. Staying "good friends" means you don't have to miss them so much. Chances are that this friendship is also painful for his ex and you already know she didn't want to lose him and tried to get him back when he was starting to see you. Seems likely she is still hoping she has a chance.
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The research tells us that compared to platonic friendships, friendships with ex lovers have lower levels of emotional support and trust and sharing of good news. In other words the costs outweigh the benefits. Add to this the unhappiness of a current partner with the arrangement and I think the answer is clear in your situation.
Your boyfriend is unwisely disregarding the fact that his minimising of how much this matters to you is putting your relationship future at risk. All up, there would seem to me there are no winners here. Trust your feelings of discomfort and let your boyfriend know very clearly that this arrangement is not okay for you. He needs to let his ex go so that she can love again. And very importantly for you, he needs to demonstrate how much he values you by listening properly to your feelings.
Perhaps this is an opportunity for him to become a bit more insightful and in touch with other peoples needs.