This answer is focused on the example of Elizabeth I as its what I have knowledge of, I hope someone can come along with other examples as its an interesting question in general.

Societies are built on shared accepted premises, and certainly one of the premises Tudor-era England operated on was the idea of men as superior to women. However, there were others that are important to consider here. The importance of the monarch as a source of authority, for example, and the hereditary nature of this authority. This wasn't just of interest to the monarch and their immediate family, but to basically any aristocrat or noble, as ultimately their power originated from the same set of assumptions about a hierarchical society and hereditary power.

They could play with the rules of course, and did, frequently, such as during the Wars of the Roses or after the Glorious Revolution, but even in these instances some semblance of hereditary continuity had to be maintained. When Edward VI died all four even remotely plausible claimants were women: Lady Jane Grey (who Edward favoured before his death but had the weakest claim), Mary Queen of Scots, Mary Tudor and Elizabeth Tudor.

So short of seriously subverting the basis of royal authority (and presumably plunging England back into the chaos which had ended in 1485), the lords and nobles of England essentially had to get used to the idea of a woman on the throne, and back the one that best suited their interests.

Jane Grey's attempt at seizing the throne fell apart fairly quickly, leaving Mary as Queen as the oldest daughter of Henry VIII, but she reigned for only five years before she died childless, and her reign was marked by severe discontent amongst Protestants due to her marriage to Phillip II of Spain and brutal persecution.

With memories of Catholic persecution fresh and the only alternative the Catholic Mary Queen of Scots, it isn't hard to see why the Protestant Elizabeth, who was also free of entanglement with Scotland or Spain, was supported heavily by English Protestants. They were still aware of the fact she was a woman, and the potential problems this could have caused however, but they actually used it to her advantage in portraying her as embodying the desirable Protestant characteristic of awareness and mastery of one's weaknesses. This essay explores how Protestant supporters of Elizabeth crafted an image for her whereby she essentially represented all of the 'best' aspects of womanhood, while Mary represented the 'worst', contrasting the supposed purity of Protestantism against the supposed corruption of Catholicism. Elizabeth herself would use similar rhetoric in the famous Tilbury speech where she admits to having the 'body of a weak and feeble woman', but claims 'the heart and stomach of a King'.

So to sum up and put it glibly: in the case of Elizabeth I, a situation arose where basically all plausible claimants were women, and Elizabeth was successful mainly on the back of being seen as not as bad as the rest. Her supporters then made a virtue of her sex however by portraying her as 'the right sort' of woman.