Looking back on Puritans, it’s easy (and common) to just say that they were uptight, incredibly strict, unbearably constricting, and that their ways of life were a thing of the past. However, that's not always true. Elements of the Puritan lifestyle and social norms are present in modern cultures and societies today.
“Modern Puritanism” still exists in the sense of a theocracy and having no separation between church and state is really prevalent in the Middle East. Sharia, or Islamic law, has a huge influence on the laws and constitutions of Islamic nations. For example, countries like Saudi Arabia, Yemen, Iraq, Iran Pakistan, Afghanistan, and Algeria have no separation between church and state. All laws and crimes are judged and according to sharia. A strong parallel to the Scarlet Letter is that civil and social functions are also governed by sharia.
Another parallel exists between sharia and the theocracy of Puritanism seen in The Crucible and The Scarlet Letter: a new generation starting to break off from the traditional system. Muslim countries, like Egypt, who have just overthrown the previously super strict regime are struggling with ideas of secularity and sharia in the drafting of their new constitution. The newer generations are considerably more "Western" and secularly minded, and they are starting to diverge from the traditional laws and constrictions of sharia.