You posted something similar in another thread. I don't think your bf should be talking to his ex, especially if it makes you uncomfortable. He should take your reasonable feelings into account. Regardless of what he says, he appears to want to have an affair with her, and appearances are important, since people do not have ESP.
This should make you ask yourself: "Is he getting everything he needs from me?" If the answer is "no", then try to think about how to improve your relationship with him, so he has no NEED to sleep with someone else.
I have a long time interest in psychology, specializing in relationship dynamics for 30 years.
(Please note, we give the best advice we can based on the information given in a post. For better advice, please include the age of all romantic partners.)