Are you speaking of your own attempts to ignore Romans 13?
Quite the contrary, I'm aware of its full context.
If you are any expert with the Bible, you'll think of Shadrach, Meshach, and Abednego. In Daniel 3.
In it, King Nebuchadnezzar ordered them to bow down before a statue of gold made in his likeness. Up until that point they had been law abiding citizens in Nebuchadnezzar's realm, nor did they directly challenge his authority. But in this instance, the Ten Commandments applied. Thou shalt not make for thee any graven image. They refused, even knowing that doing so would be at the pain of death, they knew obeying the king's order would have been direct disobedience to God's command.
They were thrown into a fiery furnace for their disobedience, but God, knowing they had stayed true to his command, protected them from certain doom. This is an example where it is God's will not to heed the governing authorities.
Also, you would have also considered Acts 4. In it, the Sanhedrin demanded that Peter and John stop preaching the name of Jesus. But obeying such a command would have constituted disobedience before God. Though they did not openly challenged the authority of the Sanhedrin, they made it clear they could not stop preaching the gospel.
"And when they had summoned them, they commanded them not to speak or teach at all in the name of Jesus. But Peter and John answered and said to them,"Whether it is right in the sight of God to give heed to you rather than to God, you be the judge; for we cannot stop speaking what we have seen and heard."
-Acts 4:19-20
So, they went on preaching the gospel despite the order, and were arrested again by the Jewish authorities for disobedience. And in another of your oversights, Acts 5:28-32, when the Sanhedrin asked why they did not obey:
"Did not we strictly command you that you should not teach in this name? And, behold, you have filled Jerusalem with your doctrine, and intend to bring this man's blood upon us. Then Peter and the other apostles answered and said, We ought to obey God rather than men. The God of our fathers raised up Jesus, whom you slew and hanged on a tree. He is who God has exalted with his right hand to be a Prince and a Savior, for to give repentance to Israel, and forgiveness of sins. And we are his witnesses of these things; and so is also the Holy Ghost, whom God has given to them that obey him."
When the Sanhedrin heard their reply, in Acts 5:33-42 they conspired to kill them. However, one of the Sanhedrin, Gamaliel convinced the council not to execute them. They were instead beaten and once again commanded not to preach in Jesus' name. They rejoiced, being happy to be counted as worthy to endure suffering for the Lord's sake. However, once again, they disobeyed, going into every house and temple preaching the name of Jesus:
"When they heard that, they were cut to the heart, and took counsel to slay them. Then stood there up one in the council, a Pharisee, named Gamaliel, a doctor of the law, had in reputation among all the people, and commanded to put the apostles forth a little space; And said unto them, You, men of Israel, take heed to yourselves what you intend to do as touching these men. For before these days rose up Theudas, boasting himself to be somebody; to whom a number of men, about four hundred, joined themselves: who was slain; and all, as many as obeyed him, were scattered, and brought to nought. After this man rose up Judas of Galilee in the days of the taxing, and drew away much people after him: he also perished; and all, even as many as obeyed him, were dispersed. And now I say unto you, Refrain from these men, and let them alone: for if this counsel or this work be of men, it will come to nought: But if it be of God, you cannot overthrow it; lest haply you be found even to fight against God. And to him they agreed: and when they had called the apostles, and beaten them, they commanded that they should not speak in the name of Jesus, and let them go. And they departed from the presence of the council, rejoicing that they were counted worthy to suffer shame for his name. And daily in the temple, and in every house, they ceased not to teach and preach Jesus Christ."
You failed to consider Exodus 1, in which the Egyptian Pharaoh commanded the Hebrew midwives to kill all the baby boys; for he feared the Hebrews would grow strong enough to resist him. But the midwives did not obey, and God blessed them with families. This is another example for which not submitting to the governing authorities was the will of God, not of your idol, Paul.
This example would be another of the more recognizable ones in the Bible. In the book of Daniel, chapter 6, King Darius decreed that for 30 days, no man could petition to any god, with exception to Darius himself. Daniel, being one of Darius' three chief presidents, in verse 10:
"When Daniel knew that the document had been signed, he went to his house where he had windows in his upper chamber open toward Jerusalem; and he got down on his knees three times a day and prayed and gave thanks before his God, as he had done previously."
When he was caught, Darius had Daniel thrown into a pit of lions to be devoured. However, God sent an angel to cull the wrath of the lions, thereby saving him from his demise. This is yet one more example of God approving of Daniel's resistance to the governing authorities, just as God saved Shadrach, Meshach, and Abednego from the fiery furnace.
Perhaps you forgot to read 1 Corinthians 2:8, where Paul himself knew full well that leaders of governments were not keen to the wisdom of God, or else they would have not crucified Jesus on the cross:
"None of the rulers of this age understood the wisdom of God; for if they had, they would not have crucified the Lord of glory."
Another, final example you failed to consider was 1 Peter 2:11, an instruction from Peter:
"Beloved, I urge you as sojourners and exiles to abstain from the passions of the flesh, which wage war against your soul."
Should I rob Peter to pay Paul?
In sum, this is why Romans 13 is not the end-all-be-all. There are times when it becomes necessary to obey God rather than men. There are limits to our obedience, and you, of all people, who make a hobby of reading the Bible, should understand the dilemma this places Christians in. These are all examples of God allowing his followers to disobey the governing authorities. God, not Paul, is the ultimate authority.
Perhaps you don't know the Bible as well as you think you do.
1) Daniel is the Old Testament- which as Christians are often want to tell me when we discuss other books of the Old Testament was the Old Testament- while the New Testament- is duh- the teachings of Jesus.
2) Same with Acts of course- in particular since Jesus challenged the Jewish priests.
3) Same with Exodus- which of course was the story of God's commandment to Jews- while Paul spoke to all Christians, including gentiles.
4) Finally- you get to Paul- which is fascinating because Paul in Romans 13 said that authority- leaders- are appointed by God- and act according to the will of God. Congratulations you have found an apparent contradiction in the Bible.
5) And Peter- another NT example- great. Here is the quote from the translation- note the quote in red below:
11 Dear friends, I urge you, as foreigners and exiles, to abstain from sinful desires, which wage war against your soul. 12 Live such good lives among the pagans that, though they accuse you of doing wrong, they may see your good deeds and glorify God on the day he visits us.
13 Submit yourselves for the Lord’s sake to every human authority: whether to the emperor, as the supreme authority, 14 or to governors, who are sent by him to punish those who do wrong and to commend those who do right. 15 For it is God’s will that by doing good you should silence the ignorant talk of foolish people. 16 Live as free people, but do not use your freedom as a cover-up for evil; live as God’s slaves. 17 Show proper respect to everyone, love the family of believers, fear God, honor the emperor.
Of course Peter was also telling Slaves to submit themselves to their masters....I don't think Peter supports you quite the way you thought he did.
18 Slaves, in reverent fear of God submit yourselves to your masters, not only to those who are good and considerate, but also to those who are harsh. 19 For it is commendable if someone bears up under the pain of unjust suffering because they are conscious of God. 20 But how is it to your credit if you receive a beating for doing wrong and endure it? But if you suffer for doing good and you endure it, this is commendable before God. 21 To this you were called, because Christ suffered for you, leaving you an example, that you should follow in his steps.
So to recap:
Paul in Romans 13 tells Christians to obey authority because they are appointed by God.
Peter in Peter 2 tells Christians to submit yourselves to every human authority.
The New Testament clearly tells Christians to obey the law.
Where in the Bible does it say "Ignore the law- and don't bake a wedding cake for Gays"?