This respectably married woman is a folklorist in Ankh-Morpork who is keen on preserving the more, er, reputable of bygone folk pathways. She is ever-vigilant in spotting smut and editing her source material to preclude any possibility that it contains anything that the ears of children, young maidens and respectably married women, such as herself, might find unseemly. To her surprise, people quite often don't see what is so reasonably offensive about old folk songs and Hogswatch anthems, until she has meticulously pointed out, step-by-step, wherein the filth may be found.
In Hogfather, she leads a group of Hogswatch carollers, known as the Ankh-Morpork Wassailers, in public singing of her new and reformed carols, collecting money as they go for the city's more grateful, picturesque, and less smelly poor, the ones who can be relied upon to tug their forelocks and say "thank you, ma'am", as is befitting. But they encounter examples of the city's undeserving poor, and are sore embarrassed by them...
Mrs Huggs stands in a long line of reformers and rewriters who, in more refined ages, refuse to believe their forebears were as rude and rustic as that, thank you very much, and set about rewriting the source material to make it more fit for modern ears. We have Thomas Bowdler, for instance, who in Victorian England took it upon himself to rewrite Shakespeare, carefully excising all the improper and over-licentious bits lest they inspire others, weaker than him, to unseemly and indecent thought and behaviour. Thus does English get the word bowdlerize to denote this sort of censorship. And before Bowdler, a fictional character called Mrs Grundy became an eponym for women of the Huggs inclination.
In more recent years, the would-be social reformer Mrs Mary Whitehouse fought a campaign to clean up what she thought of as the debasing and degrading medium of television, viewed by her and her acolytes as bringing unbridled sexual filth and disgusting left-wing politics into every home in the land. As a sideline, she had a serious theatrical work banned under the archaic and centuries-old laws of blasphemy, the first such charge brought in the UK for a couple of hundred years.
After much searching and head-scratching, I have finally found the equivalent of Mary Whitehouse whose name will make sense to American readers. I knew there was one! However, it's not a she - it's a he. The arch-prude for the United States was a certain Mr Anthony Comstock, who operated as a moral decency crusader between 1873 and his death in 1915. He brought indecency actions against art galleries, forced the owners of underwear shops not to display their wares in the window lest they provoke licentiousness, deplored silent movies as pornographic and degrading, and even had the United States legislature enact its second-most risible attempt to regulate human behaviour(after Prohibition). The Comstock Act was passed in 1873 after a mere ten minutes' debate in Congress, and gave Comstock absolute power to regulate the United States Mail, opening all mail if necessary and searching it for filth and depravity. America appears to have a knack for putting people of this mentality in positions of power: Senator McCarthy and J.Edgar Hoover (a disciple of Comstock, incidentally) come to mind, as does Supreme Judge Potter Stewart, who in 1973 redefined United States obscenity law with the considered legal judgement "I know it when I see it".
Anthony Comstock also served, all his life, as Founder and First Secretary of the Society for the Suppression of Vice.