It's not exactly Tudor, but Mary I did marry her cousin Philip I who was a Hapsburg, and this does relate to this question.
In an answer to the question about Elizabeth of York's pregnancy, it was explained that Henry VII and Elizabeth had to wait for special dispensation from the pope because they were related.
The Hapsburgs intermarried, but their marriages were between couples that were much more closely related than Elizabeth and Henry VII. Did they also have to get papal dispensation, or could they do without it because they were Holy Roman Emperors or relatives or the HRE? Did a couple always have to get dispensation when they were related, or was it sometimes overlooked?