From the legal view rhaenyra was not the dominant claimant, stannis would follow that view. Oddly enough its a self fulfilling sexism in medieval and feudal society, a woman could not (some exceptions exist) lead armies or defeat enemies, The Anarchy was specifically because people didn't trust the queen to be able to handle the realm, and her opponent was a valiant fighter who lead the armies. For the job of the time, men were more suited and westeros follows the same line to varying degrees. The powerful women of the time got good at intrigue and states craft to compensate, brain vs brawn in a brawn centric world. Cersei played the game in that same way, cant use a sword so outthink the men

Stannis did emphatically want shireen to sit in the throne should anything happen to him, it was her right etc