If I use Escape Rope but my opponent's Active Pokemon has the "Omega Barrier" Ancient Trait does he or she have to switch it? Or if they have a Pokemon with "Omega Barrier" on the bench can he or she choose that and not switch it to Active?

If your opponent has an Active Pokemon with "Omega Barrier", then Escape Rope's effect will be blocked. If a Pokemon with "Omega Barrier" is on the bench, choosing that Pokemon will not stop the effect as the Active was the target of Escape Rope.

Relevant cards

XYP_XY49