Only you know what is right for you!
Having said that there should not be any "double standards". In other words if it's fine for you to remain in contact with your ex then it should be fine for your mate to remain in contact with their ex.
Situations like this have nothing to do with "right" or "wrong" and everything to do with "agree" or "disagree". Ultimately the goal is to find someone who (naturally) agrees with us on things we consider important. When you disagree one of you has to decide whether or not if it's a "deal breaker".
Generally speaking most people do not seek out a mate to "change" them. They want to be loved and accepted for who (they) are. If someone believes in staying in contact with exes and their mate does not want them to then they have decide if they want to change their ways/life for the person they're (presently) dating.
Suppose this relationship ends, do you get back in touch with your ex because your new mate doesn't have a problem with it? Life is much easier if you always stay true to yourself instead of reinventing yourself each time you get into a new relationship.