The Rema’s shita is a chumra, period. He holds like one rishon, while the Beis Yosef/Mechaber holds like all the other rishonim. Ashkenazic stringency does not equal halakha.
Are you calling the Mechaber incorrect? Do you pasken like the Rema when he says that you can hold a wedding on Shabbat and that it is mutar to drink wine made by goyim in places where that is customary? Stop being foolish now.