“Yet they are a major part of the ceremony. Strange.”
It isn’t strange. It is just a category mistake of logic.
There is no Biblical marriage ceremony. No one purports rings are Biblical. No one prances around flashing the ring to try to identify themselves as a spiritual class of believer.
Against this...
5“But they do all their deeds to be noticed by men; for they broaden their phylacteries and lengthen the tassels of their garments. 6“They love the place of honor at banquets and the chief seats in the synagogues, 7and respectful greetings in the market places, and being called Rabbi by men. 8“But do not be called Rabbi; for One is your Teacher, and you are all brothers.
Nobody is purporting vestments as un-Biblical, except you. So when I see you railing against all the other un-Biblical things Christians do in church I might take your argument seriously.