Just an update. Ancestry support reached out to me because they're investigating this bug, and they believe it was caused by the "link to Facebook" option, and that the bug is now resolved.
Just before the sync that went wrong, I had linked to Facebook, then changed my mind and undid the Facebook link. I don't know if it was the linking or unlinking that triggered the problem.
I'm impressed that tech support reached out on the basis of this forum thread alone, without me making a bug report.