I’m really interested in what shifted from Elizabeth of York (daughter of a king with no living brothers) only being considered to bolster the claim of her husband to Elizabeth I (daughter of a king with no living brothers) ruling successfully in her own right.
When Elizabeth of York's father died, she had living brothers. Edward V ascended the throne upon his father's death (though he was never actually crowned) and his uncle, the Duke of Gloucester, or Richard III as he came to be known, was declared his Lord Protector. However, before he could have his coronation, the marriage his father had before his death to Elizabeth Woodville was declared invalid and to be bigamous, as supposedly he had in fact already been betrothed to another - the daughter of the Earl of Shrewsbury, John Talbot. This then made any and all children from Edward IV's marriage to Elizabeth Woodville bastards and their claim was considered to be illegitimate.
When Edward V and his younger brother (the 'Princes in the Tower', as they are famously known as) disappeared and were presumed dead, Richard III ascended as the eldest male relative, with a 'true' claim to the throne. He was declared to be the rightful heir to the throne.
Elizabeth of York and her marriage to Henry VII was very carefully orchestrated by Margaret Beaufort and Elizabeth Woodville. It served to unify the two houses and bind them in an alliance.
Elizabeth I however, was a legitimate daughter of Henry VIII. There was no disputing her claim, and after Edward VI's death, and the deposition of Lady Jane Grey and finally Mary's death, she was the only legitimate heir to the throne - Henry of course, had no living brothers. Many people believed that it was the divine and God who decided upon the monarchy, and thus a woman could be queen in her own right. However, Elizabeth was STRONGLY encouraged by her privy council and those close to her to take a husband - her sister, Mary had obviously married Phillip of Spain. She had seen how her sister's power was limited, numerous historians have argued, with her marriage to Phillip. She refused to take a husband and continued to rule in her own right.
To answer as to what shifted, I do not think it was a shift, so much as the events at the time allowed both realities to happen. Elizabeth of York had her claim stripped from her when she was declared a bastard, however there was no such event leading up to the reign of Elizabeth I outside of Edward VI removing his elder sister Mary from the succession to the throne.
I hope this helps you a little!