Those are not examples of conflicting rights. Those are examples of things that are not even covered by rights.Wrong. You do not have a right to carry a firearm if you’re a convicted felon. You don’t have a right to posses firearm in a public place that informs to stipulated gun free areas by state, local and federal decree.
You don’t even have a right to go anywhere and say anything* you want in a private place without permission. You can’t practice many of your rights in my domicile if I don’t want you to. It’s quite simple. My rights supercede yours in many cases.
Also, non-violent felons do have the right to carry guns. Hopefully soon the Supreme Court will start enforcing that.