Female regents were common, and some regents exercised significant power in that role. The French monarchy specifically only acknowledged patrilineal succession, so in their eyes, the divine right to rule didn't pass through females. That little tidbit helped start the 100 Years War with England. There was no rule against a Queen in her own right in England or Scotland, but it wasn't preferred and didn't really come up until the respective deaths of Henry VIII of England and James IV of Scotland.

Empress Matilda was supposed to Queen Regnant after her father passed but her male cousin stole the throne. She'd acted as regent on behalf of her husband in Germany though when he was away. Catherine de Aragon did the same for Henry VIII, as did Katherine Parr for a short while.

Catherine de Medici of France was regent for her children, Margaret Tudor was for a hot minute till she made bad decisions in Scotland, Marie de Guise acted as regent in Scotland for her daughter Mary of Scots. Earlier than that Isabella of France was regent for Edward III.

There were Duchess Regnants, not regents, who were the de facto queens of their territories, such as Marie of Burgundy.

Mary I and Elizabeth I became the first proper Queen Regnants of England because they were next in the succession and had no male relatives. Edward VI had nearly bypassed them, but that was due more to religious reasons and shady council.

There were definitely people like John Knox who couldn't tolerate the idea of women ruling, but other than France it wasn't against any rule.

(All links in this post are to past answers of mine.)

To my understanding, before Queen Anne, there weren't many queens in the UK. The monarchy would pass over any woman in order to find a distant male heir.

This is not actually true. Is there a particular succession crisis that you're thinking of? This was true of France, following the problematic succession of Philippe VI, but it was not the practice to do so in England/Great Britain. As /u/Forgetful_Panda has noted, Empress Matilda was usurped successfully by a male cousin - this was not inherently because people didn't want a queen, as her father's barons had accepted her willingly as his heir and sworn their oaths to her, but because Stephen decided to swoop in and Matilda remained in France for several years. Other succession crises happened similarly as a result of deliberate usurpation: Henry IV, Edward IV, Henry VII.

Before Anne, there was also Mary, Elizabeth, and Mary II, plus the disputed claimants Jane Grey and Mary Stuart. The reason that these women became queen, or were in a position to say they should be queens, is that they were the appropriate next heirs. (Well, it's more complicated than that with Mary II, but.) It should be noted that there simply weren't any male cousins they could be passed over in favor of, but there was no precedent for daughters of the king to be passed over in favor of nephews.

But then suddenly, after Charles I, it's like having a queen was all the rage both in Britain and many other parts of the world?

It was actually normal for women to become queens if they were the next in the line of succession even before the eighteenth century in other European countries:

There were a few European queens regnant in the fifteenth century. Margrethe I of Denmark (1353-1412) ruled Denmark, Sweden, and Norway from 1387 until her death; she was elected queen following her son's death, as she had been his regent when he was a child, and while she named another king to follow her son as king of Norway, she acted as regent for him in his minority as well, and effectively ruled all three kingdoms through much of her adult life. Joanna II of Naples (1371-1435) succeeded her brother in 1414, and while she married very soon after, her husband revolted against her and lost, becoming a powerless consort.

There was even more precedent in Spain, or rather, in Iberian kingdoms, since a united Spain didn't really exist until after Isabel. Navarre in particular had had several medieval queens: Juana I (1273-1305), who came to the throne as an infant and allowed governors to rule Navarre when married outside of the kingdom; Juana II (1312-1349), who ruled jointly with her husband; Blanca I (1387-1441), who did the same; Leonor (1426-1479), who unfortunately died almost immediately after being recognized as queen; Blanca II (1424-1464), who was imprisoned by her family when others declared her queen and was never able to act on it; and Catalina (1468-1517), who also ruled jointly with her husband, post-Isabel. Léon also had a major one before Isabel: Urraca (1079-1126), who ruled jointly with her husband. Aragon had Petronilla (1136-1173) and Castile had Berengaria (1179-1246), both of whom abdicated in favor of their sons. (And outside of these examples, Iberia had strong traditions of officially mandated queen-lieutenants who ruled in their husbands' stead when the king was ill, on crusade, in battle, etc.) When I say "ruled jointly", what I mean is that it was accepted that their husbands should also be crowned as a ruling monarch - elevated to kingship - rather than seen as consorts in the way that queens who married into a ruling family were, and this can encompass anything from "the king and queen were truly equal co-monarchs" to "they were both crowned, but he acted as head of state and she acted as a consort".

Again, it's just France where people were willing to go through contortions to find a male heir specifically.

I'd also point out that John Knox, who wrote The First Blast of the Trumpet Against the Monstrous Regiment of Women, was specifically incensed about the Catholic queens in power at the time he wrote it - Mary Tudor and Mary Stuart - as he was a staunch Protestant. He was perfectly fine with Elizabeth (although she wasn't perfectly fine with him because he'd written a misogynistic pamphlet that could be used against her own right to rule).