The Lord Jesus warned His people to beware three kinds of yeasts (ideas, teachings): Phariseeism, Saduceeism, and Herodianism (Matthew 16:6, Mark 8:14-15).
We know pretty well what the Pharisees and Saducees were about. But what was Heordianism? We can only piece a picture together by looking at the life and behavior of the Herods, who were the Edomite kings appointed by Rome over Israel.
Herod the Great was a man who prized political power above all else. He even went so far as to try and murder the Messiah, the Lord Jesus, when Christ was born. He had all the boy babies in Bethlehem two years old and under killed, in a cruel attempt to wipe out the Messiah.
Herod killed all his sons, because of he was suspicious of their intentions toward his throne. Caesar once said you'd be safer as Herod's pig than as his son. Nothing mattered more to Herod than political power.
The next Herod, Antipas, was a man who thought he was above the law. He married his brother's wife, for which John the Baptist publicly censured him. This is what got John martyred. Herod had a fitful, inconsistent regard for John, but his resentful wife schemed up a way to manipulate him into executing John.
That incident showed that Herod prized image over integrity. Herod had put his public image on the line by promising Salome' anything in exchange for her erotic dancing. The court and foreign visitors were all present, when Herod (probably drunk, and inflamed with lust) crawled out on that limb. So, when the girl demanded John's head on a platter, Herod did it.
Herod bought the compliance of the people of God. This Herod is renowned for his building projects, chief of which was the re-building of the temple. By these means Herod maintained a fragment of peace between his administration and the restless, resentful Jews. It was a transactional relationship: Herod would do A, B, or C for the Jews, and their leaders would suppress unrest. Bribery was Herod's standard operating procedure.
Herod was, despite his public posturing, a godless man. In spite of the millions he spent on the temple project, Herod treated the Lord Jesus first with empty curiosity, and then with contempt. He was willing to allow a crowd to hail him as a god (Acts 12:22), for which God killed him (v.23).
God sometimes enables His servants to work in government service, or influence government policy. We know of Bible greats who served God in government, like David, Daniel, Esther, and Nehemiah. So it isn't a sin to serve in government.
But there are temptations in politics that are unique to it. The Pharisees were middle-class religionists who exalted tradition over scripture, ceremony over godliness, and works over grace. The Saducees were religious elitists who welcomed pagan philosophies (in their case, Greek), and tried to adapt the Bible to the latest trends.
But the unique temptations of politics are to worship power; to justify sinning in the name of a supposed greater good; to use one's position to indulge and enrich one's self; to worry more about losing face than losing God; and to use the religion of Jesus Christ to advance completely secular goals (thus corrupting it).