You are absolutely right: our rights are a gift from God, not a grant from the government. However, in traditional Catholic theology, the civil government is the lawful avenger of crime, as it derives its just powers from God.
Loss of the right to vote and the right to own a gun are logical penalties for violent felonious crimes and are not inconsistent with God-given rights possessed by innocent and law abiding citizens.
Logical or not, Inconsistent or not .. it is not the governments job to guess which Right God would approve of taking away!
And .. the Constitution was not written with Catholic theology in mind!