What matters here is that distinguishing between a legitimate concern and emotional control is complicated, but the key is in how you communicate. If your boyfriend simply tells you "this makes me uncomfortable" and then respects your decision even if he doesn't like it, that's different from him giving you an ultimatum or getting upset every time you mention your ex. Discomfort in this type of situation is normal - lots of couples feel insecurity about exes - but what sets a healthy relationship apart is how you negotiate it.
Ask yourself some things: how frequent is the contact? Is it completely platonic or is there something that doesn't quite feel right? Does your boyfriend have specific reasons to distrust you or is it just insecurity? Because there's a middle ground between "cut all contact or we break up" and "do whatever you want with no limits." You could agree that the friendship exists but keep it low-key, don't share couple stuff with your ex, or just let him know when you're going to talk to that person. That's not giving up everything, it's showing that you respect the current relationship.
What's important is that you also have a voice in the conversation. If you feel like your boyfriend is controlling in other things too - telling you who you can talk to, where you can go, etc. - then there's a bigger problem. But if it's just this one thing, it's worth having a calm talk where you explain why that friendship matters to you and actually listen to why it makes him insecure. Sometimes the solution isn't cutting contact or letting him do whatever he wants, but understanding each other better.