The son, Henry The 8th.

I guess Lancasterian would be an easy no, considering they were few and since Henry VIII was a Lancasterian himself from a paternal line, he would be seen more affiliated with them "one of us" from their point of view.

Yorkist would also see this as the same, considering how his mother, Margaret of York, would've been heir to the throne with the death of her father Edward, uncle Richard III and her brothers, the two princes, had it not been for Henry VII's cutting in line and placing himself as King, yet since the son of Margaret would be the next ruler regardless of who the father was, even if that was Henry VII himself, it's easy to also see why the Yorkist also support him.

But were there any Lancasterian/Yorkist loyalist who didn't see it this way? Perhaps a Lancasterian saw Henry VIII as more affiliated with the Yorkist? Or a Yorkist saw Henry VIII's blood as tainted with Lancasterian blood, and therefore was not a 'pure' Yorkist? Has been any recorded source where it was expressed that there was still doubt on Henry VIII's legitimacy as King due to his father's background?

What do you suppose would have been the case had a 'pure' Yorkist arrived at the scene, perhaps one of the princes of the Tower of London? Would you think that people would view them as more legitimate, assuming that they accept they are real princes of the tower?