I think you're being a
bit anachronistic reading the separation of the civil and the religious back into the First Century. The emperor was likely also to be
Pontifex Maximus (I'm not sure whether they all were); Herod I appointed nonentities as High Priest, probably in order to keep the Temple under control, and not long before the
Hasmoneans had been High Priest and, in some cases,
king. The
Roman governors of Judea kept the High Priestly vestments under lock and key except during the major festivals, doubtless again in order to control the Temple.
The first Christians were realists who knew they
had no chance of influencing the state, except possibly to get it to treat them a
bit better, and many of them didn't care anyway, since they were convinced Jesus was coming back any day to put an end to all that nonsense and inaugurate the Reign of God.
I think there are two plausible readings for the story. One, if you assume it originates with Jesus, or at least about
his time, is a question as to the legitimacy of
Roman rule over the Jews. Deuteronomy 17:15 bans the Israelites from having a foreign
king. Probably the crunch came with Quirinius'
census in late 6 or early 7AD, and the taxation that followed it. Judas of Galilee revolted, and according to Josephus, founded the nameless 'Fourth Philosophy' which later influenced the First Revolt.
Josephus says:
These men agree in all other things with the Pharisaic notions, but they have an inviolable attachment to liberty, and say that God is to be their only Ruler and Lord. They also do not value dying any kinds of death, nor indeed do they heed the deaths of their relatives and friends, nor can any such fear make them call any man lord; (
Antiquities of the Jews 18:23). These sound like radical Pharisees, but whatever their origin, they clearly didn't accept the legitimacy of
Roman rule, and, given the origins of the movement, may well have been reluctant to use
Roman coinage or pay tax to
Rome. If Josephus is to be believed, they were around in Jesus' day, but there was no organized resistance at the time. We do have evidence of individual 'rebels' (lestes), but these may well have been little more than bandits. But the beliefs of the 'fourth philosophy could plausibly have given rise to the question.
The other possibility, if you hold, as I do, that the Gospels are the product of later
Christian communities, and represent theology rather than
history, relates to Vespasian's
fiscus judaicus, introduced after the destruction of the Temple. The was levied at the rate of 2 drachmae
per man and was equivalent to the earlier
Temple Tax. It was paid to the temple of
Jupiter Capitolinus, but whether this was a deliberate insult, or whether it was because the temple acted as the imperial treasury, isn't clear. Mark appears to have been written after 70, probably during the 70's, and thus at a time when the tax may well have been controversial. Christianity was a
Jewish movement, and was probably recognized as such at the time; the Jews only appear to have begun to reject it in the 80's. Mark was written for a largely Gentile community, however, so should that pay a tax intended purely for Jews? It would have been a potentially divisive issue when the
church included both Jews and
Gentiles, and one way of settling it might have been to put an appropriate saying in Jesus' mouth.
Which reading a person prefers will doubtless depend on their beliefs, but that is theology, and has no place here!