Two Christian sources before AD 249-251 took a more lenient view as to what sorts of government posts were forbidden.
A manual of Christian personal and corporate life, titled “The Didascalia”, was produced in Syriaduring the first decades of the third century, roughly the time when the writing ministries of Tertullian and Origen overlapped. Chapter 18 forbids accepting gifts for widows, orphans, and the church from what the Didascalia considers the worst of sinners, including “Roman officials, who are defiled with wars and have shed innocent blood without trial”, “dishonest tax-collectors”, and “soldiers who act lawlessly”. What was prohibited here is not employment by the government per se, but abuses of authority in the course of a necessary office. Remember that what John the Baptist forbade was not a person being a tax-collector, but taking more money than authorized and pocketing the difference; John prohibited not military service, but only violence and looting (Luke 3.12-14). (Both these sources differ from Tertullian, Origen, and Hippolytus, who banned any species of military employment.)
In AD 217 Bishop Hippolytus in central Italycompiled a similar manual of existing church practices, which had allegedly descended from the apostles, in order to guide clergy in correct practices and to enable laity to detect and take action against deviations. It excludes only some categories of secular office-bearers from the church, which presumably means other categories of politicians and bureaucrats were welcome, and thus lays down no blanket prohibition to believers from seeking to serve the state.
The first-listed forbidden office was public officials involved in gladiator shows (Apostolic Tradition 16.15)—naturally enough, because such events involved putting to death for public entertainment people who had committed no crime. In fact, Tertullian wrote an entire book against them and other blood sports and amusements.
Hippolytus’s manual also denied church membership to soldiers who kill (16.17), and to military governors (16.18)—again to be expected in light of other Christian writings that forbade military service and homicide of any sort, even volunteering for the armed services (16.19). Also rejected were city magistrates that wore purple togas as symbols of wealth and high secular office (16.18).