+Not sure if I understand/
I believe the last element of due process is the right to appeal. That may be done with an attorney or self filing, or with the assistance of a “jail house lawyer” a legal term.
Not sure if an appeal is a petition, but may be.
I was addressing the right to petition public officials (Governor, Corrections commissioner etc.) which would be separate from a legal appeal of ones case. IMO
If you want to be technical and argue that petition applies only to political entities and not to administrative or judicial ones, I would reply that such a technical objection is historically unsound: Magna Carta's guarantees were primarily procedural and not political.
But if I stipulate that I will allow you to say that due process is not what the First Amendment authors had in mind, I believe there are still examples where incarcerated prisoners are not entitled to the same privileges and immunities in that regard.
Like what?
Obviously things that incarceration itself makes impossible, like attending hearings and public meetings mandated by sunshine laws. Those are what I had in mind with my statement about how obvious it is that they don't enjoy the same right to petition. You can't come to the mike to protest an ordinance if you're in jail.
Anything else?
Well, for example, in several states convicts cannot be lobbyists [in most states the restriction is not permanent absent a pardon; it's usually for ten or twenty years.] That restriction holds, a fortiori for those actually in prison. Lobbying is recognized -- subject to certain statutory restrictions -- as a form of petition protected by Amendment I.