score:9
The Catholic Church understands these verses in the context both of the rest of the chapter and of statements made about the responsibility of public authorities in the rest of the Bible.
The New American Bible, Revised Edition, reads for Romans 13:1β2:
Let every person be subordinate to the higher authorities, for there is no authority except from God, and those that exist have been established by God. Therefore, whoever resists authority opposes what God has appointed, and those who oppose it will bring judgment upon themselves.
The chapter has a note to it, however, and the note references the Book of Wisdom, chapter 6. In particular:
Hear, therefore, kings, and understand; learn, you magistrates of the earthβs expanse! ...
Because, though you were ministers of his kingdom, you did not judge rightly, and did not keep the law, nor walk according to the will of God, terribly and swiftly he shall come against you, because severe judgment awaits the exalted. For the lowly may be pardoned out of mercy, but the mighty shall be mightily put to the test.
The interpretation the Church gives to this (see the note to the Romans text) is that
believers who render obedience to the governing authorities are obeying the one who is highest in command. At the same time, it is recognized that Caesar has the responsibility to make just ordinances and to commend uprightness; cf. Wis 6:4β21. That Caesar is not entitled to obedience when such obedience would nullify God's prior claim to the believers' moral decision becomes clear in the light of the following verses.
(emphasis added)
Thus, even if public authority commanded that every religious institution perform same-sex marriages, if the Church believed that such a command contravened the will of God, it would refuse to do so.