They would still be unhappy about being occupied by them, but the effect shouldn't be as great as if it were a completely alien culture.
Now, if a German minor for some reason became occupied by China or some Mongol country or something, then the income loss and the revolt risk should be higher than it would if it was Denmark.
The cultural difference between Scandinavian and German is really not that much greater than the difference between say, Austria and Prussia.
Ukrainian and Russian too are more closely related to each other than either are to Mongols. No, Ukraine would not be happy under Russian control, but they would certainly be far less happy under the control of the totally alien Golden Horde.