From this place we learn by the Saviour's example not to be allured by those things which have many voices for them, and thence seem famous, but to incline rather to those things which are spoken according to some method of reason. But we may also understand this place morally, that we ought to give some things to the body as a tribute to Cæsar, that is to say, necessaries. And such things as are congenial to our souls' nature, that is, such things as lead to virtue, those we ought to offer to God. They then who without any moderation inculcate the law of God, and command us to have no care for the things required by the body, are the Pharisees, who forbad to give tribute to Cæsar, forbidding to marry, and commanding to abstain from meats, which God hath created. (1 Tim. 4:3.) They, on the other hand, who allow too much indulgence to the body are the Herodians. But our Saviour would neither that virtue should be enfeebled by immoderate devotedness to the flesh; nor that our fleshly nature should be oppressed by our unremitting efforts after virtue. Or the prince of this world, that is, the Devil, is called Cæsar; and we cannot render to God the things that are God's, unless we have first rendered to this prince all that is his, that is, have cast off all wickedness. This moreover let us learn from this place, that to those who tempt us we should neither be totally silent, nor yet answer openly, but with caution, to cut off all occasion from those who seek occasion in us, and teach without blame the things which may save those who are willing to be saved.
Source: Catena Aurea by Aquinas