Turks being part of the tribe of Dan was not even part of the prophecy, just St. Hildegard remarking something that "some say". A theory in other words. Quoting someone quoting a theory is not proof for the theory.
You, apparently, lack reading comprehension and inference reasoning.
"When the great ruler exterminates the Turks almost entirely, ****one of the remaining Mohammadans**** will be converted, become a priest, bishop and cardinal..."
"He, as well as Antichrist, are descendants of the tribe of Dan."
Thus, we can infer that he is a Turk since he's a Muhammadan and almost all Turks were exterminated except himself, and he, and Antichrist, are from the Tribe of Dan as specifically mentioned by St. Hildegard.
Also, have you ever heard of the Donmeh? They're Turkish crypto-Jews.