When people really “move on” from a relationship, they really don’t care what their “ex’s” are doing–they are completely immersed in their own lives and/or relationships.
When my wife and I met, we had both been in relationships where the other parties found it difficult to “let go,” so we found that cutting off all contact with those parties worked out best–especially since we had no prior marriages.
It’s not always easy when there are mutual friends/and or family involved, but, unless their are children from a previous relationship involved–it’s really the only way to go–if, in fact, you’ve actually “moved on.”