People tend to forget that Tudor's ONLY real claim to the throne came through the Beaufort line of John of Gaunt and that its legitimacy has always been questioned.
If the princes were a threat, obviously the princess was as well — yet Richard III didn’t get rid of her.
Precisely! Richard would have had no reason to kill the Princes and allow their sisters to live. Henry Tudor's pledge to marry Elizabeth of York would have been a death sentence for her if Richard was the type of person who would murder his brother's children purely for convenience. However, Henry Tudor had every reason to murder the Princes and allow the Princesses to live.
The sister was never a rallying point for rebellion.
Male primogeniture was taken so overwhelmingly seriously that she meant nothing.