In my view, convicted offenders who are out on parole should not have all of the same rights as people who have not been convicted of a crime. The main reason for this is that a person on parole is still serving the term of punishment that they have been sentenced to for their crime. This means that they have not yet “paid their debt” to society. This does not, however, mean that they should be denied all constitutional rights.
I would argue that a person who is on parole is still being punished under their original sentence. That means they are not entitled to full rights as citizens. For this reason, I would support denying them some rights. These might include the right to carry a fire arm, the right to associate with whoever they like, and the right to be free from warrantless searches and seizures. However, I would not support denying them other rights. They must surely retain the right to freedom of religion and of speech, for example.
I would support the idea that convicted prisoners who have served their entire sentences should have all their constitutional rights restored. I would not, however, support full restoration of rights for people still on parole.