How the crucible puritanism relates to modern day puritism is the laws that they pass down and the religon today, for example christianity wants to be pure and perfect and wants you to not break what you belive in. Being christian means you don't smoke, don't do crime, don't break the law, and dress proper. It almost applies the same with modern day government, as long as you don't smoke, don't break the law for any reason you won't be put in jail.
In the Crucible, if you broke the law you would be put to death by the hands of their own government. The same rules of the government applied the same as there religon back then, but if there was dancing, rituals, or even anything that they thought had to do with the devil, and not being pure, you would be put to death.
