My boyfriend wants to continue close friendship with ex-wife?

My boyfriend of 14 months has a very close relationship with his ex wife. They share two teenage boys and talk very frequently. This all seems very normal until you throw in a few factors. My ex has told me that his ex is still in love with him and believes that they are soulmates and will eventually end up back together. He has informed me that he has been friends with her for over 20 years and has no intentions of ever stopping that friendship. He won't talk to her on the phone when I am around because he says he doesn't want me to see how he is with her. When we had been dating 2 months, they had but he insists their relationship is purely platonic now. When she needs help, he sees nothing wrong with helping her - whether it be physical or financial. I am not allowed to go to the boys' functions because she is not yet comfortable with seeing me with him. He leaves me out of everything that involves her. Please give me some feedback and let me know what you think I should do.