Does respect, due diligence, and protecting freedoms go with obedience of governing authorities? Why not vote?

We should vote. Not because there is any perfect leadership that fits Christian thinking, but choosing the least of evil.

Romans

13:1 be in subjection. This Gr. word was used of a soldier’s absolute obedience to his superior officer. Scripture makes one exception to this command: when obedience to civil authority would require disobedience to God’s Word (Ex 1:17; Da 3:16–18; 6:7, 10; see note on Ac 4:19).

governing authorities. Every position of civil authority without regard to competency, morality, reasonableness, or any other caveat (1Th 4:11, 12; 1Ti 2:1, 2; Tit 3:1, 2).

there is no authority except from God. Since He alone is the sovereign ruler of the universe (Pss 62:11; 103:19; 1Ti 6:15), He has instituted 4 authorities on earth:

1) the government over all citizens;

2) the church over all believers;

3) the parents over all children; and

4) the masters over all employees.

established. Human government’s authority derives from and is defined by God. He instituted human government to reward good and to restrain sin in an evil, fallen world.

13:2 opposed the ordinance of God. Since all government is God-ordained, disobedience is rebellion against God.

condemnation. Not God’s judgment, but punishment from the government for breaking the law

MacArthur, J. F., Jr. (2006). The MacArthur study Bible: New American Standard Bible. (Ro 13:1–2). Nashville, TN: Thomas Nelson Publishers.

Romans 13:1 Every person is to be in subjection to the governing authorities. For there is no authority except from God, and those which exist are established by God.