If your kids had a good relationship with their father then they may see the new guy as a threat to that relationship. If they didn't, they may fear that they will be disappointed by the new guy. Also it may be a protection thing toward you if the marriage was abusive. Keep in mind you haven't mentioned how your marriage was or ended. I'm just throwing ideas from my own experience so all of that might be wrong.
I agree with Nod, find out why they don't like him, and be prepared for irrational and hysterical, and just go slow let the two sides get to know each other before you make any major decisions.