Legal Question in Criminal Law in Colorado

Yes, probaton can deny you an out-of-state transfer. Presuming you disagree with the decision, you can file a request with the court and ask for a hearing.

You cannot sue, but you can ask the court to allow you to attend a more secular recovery group if you have religious objections.

When you agreed to probation, you gave up your "right to move to Oregon" during the period of probation. Mr. Cassens is right, your probation officer can RESIST the out of state transfer, but your probation is with the Court, not the PO. You can take your case before the Court. Perhaps you have achieved goals during your probation that would motivate the Court to end your probation early, or otherwise modify your probation conditions. I would assemble proofs of completion and other things that cast you in the best light, then Motion the Court to Modify Probation.