Surely you dont think the Church is subordinate to the State? Don't call me Shirley! (kidding!)
The church IS subordinate to the State in certain areas, yes. Paul taught:
Remind them to be subject to rulers, to authorities, to be obedient, to be ready for every good deed, to malign no one, to be peaceable, gentle, showing every consideration for all men. (Titus 3:1,2)
Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. (Romans 13:1)
Therefore, it is necessary to submit to the authorities, not only because of possible punishment but also as a matter of conscience. (Romans 13:5)
Peter also taught:
Submit yourselves for the Lord's sake to every human institution, whether to a king as the one in authority, or to governors as sent by him for the punishment of evildoers and the praise of those who do right. (I Peter 2:13,14)
Act as free men, and do not use your freedom as a covering for evil, but use it as bondslaves of God. Honor all people, love the brotherhood, fear God, honor the king. Servants, be submissive to your masters with all respect, not only to those who are good and gentle, but also to those who are unreasonable. (I Peter 2:16-18)
Even Jesus said to render unto Ceasar that which is Ceasar's and He paid his taxes. But, as always, we are to obey God rather than man in those cases where man's commands disobey the commands of God.