It could be that your sons miss having a dad and so, for a while, they are willing to take your xh on his terms. My boys did that until they were tired of being hurt, disappointed and embarrassed. Maybe they just accept him for who he is and know their relationship will be shallow. To me, their acceptance says a lot more about you as a mom. Clearly you've raised them to be kind and tolerant, if not fully accepting of others. If the relationship doesn't work or is hurtful they know how to walk away. Trust that.