I suppose a work around would be setting up two master pages (one with white folios and one with black), but I'm wondering if there is any other solution.
Yes, you would have to set up a different master for the white folio—it could be based on the black version. An overridden master page item continues to have a relationship to the master. So if you shuffle a right page with an overridden item to the left, the relationship is still with the masterpage item on the right page of the master spread. You can delete the overridden item or you can choose PagesPanel>Masterpages>Remove Selected Overrides
When you move pages between documents the source page's layout could change if there's a master spread with the same name in the destination document. Do the source and destination documents have identical Masterpages both in name and content?
Yes, the master pages are identical. The documents were all started from the same template, but I had to split it apart because there were so many pages.
I never switch a page from a left page to a right page, though. So in theory there shouldn't be a switch with the margins like I'm getting.
Can you post an sample?