Can my boyfriend’s ex-girlfriend keep me from being around his son?

If she gets a protection order against you, then the court is keeping you from being around his son. You will need to prove that you are not a danger to the child.

You don't say if the ex is the mother of the child. If she is, she can ask the court to put some restraints on your contact with the child if she can show such contacts are not in his best interest. A protection order would require that you have done something inappropriate.

The ex-girlfriend will only be able to get an OFP against you if you have caused her bodily harm, threatened to harm her, or threatened her life. Without evidence of such, a good defense will be able to get a judge to dismiss any petition for an OFP that she files. Otherwise, is there a court order granting your boyfriend the right to parenting time with his son? And why is your divorce relevant to the contact that she doesn't like between you and her son? These questions need to be answered before it will be known whether she can keep you from being around your boyfriend's son.