No one thinks that. JC would have never been in politics to begin with, considering the nature of the job. "What is caesar's, belongs to Caesar".
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1. Everything Jesus did was political at the time. Israel was a theocracy, there was no separation of church and state. In fact, the entire concept of separation of church and state would have been incomprehensible to them at the time. If you criticized religious authorities, then you were involving yourself in politics.
2. Let's look at the verse you paraphrased in context:
Matthew 22:15-22
"Then the Pharisees went and plotted to entrap him in what he said. 16 So they sent their disciples to him, along with the Herodians, saying, “Teacher, we know that you are sincere, and teach the way of God in accordance with truth, and show deference to no one; for you do not regard people with partiality. 17 Tell us, then, what you think. Is it lawful to pay taxes to the emperor, or not?” 18 But Jesus, aware of their malice, said, “Why are you putting me to the test, you hypocrites? 19 Show me the coin used for the tax.” And they brought him a denarius. 20 Then he said to them, “Whose head is this, and whose title?” 21 They answered, “The emperor’s.” Then he said to them, “Give therefore to the emperor the things that are the emperor’s, and to God the things that are God’s.” 22 When they heard this, they were amazed; and they left him and went away."
The passage has nothing to do with a separation of church and state. The religious authorities were constantly trying to get Jesus to commit sedition. In this case, Jesus was simply being clever to avoid committing sedition. Basically, he asks them "Who is on this coin?", to which they answer the emperor, and he said "Well, it's his then, so give it back to him."
BTW, how passages in the Bible do you think there are on helping the sick and the poor? The answer is over 2000, it is the most common subject in the Bible.
