Minor nitpick/footnote: the Pharisees weren’t as strict as people often assume. Heck, the Essenes had a lot of elaborate regulations far stricter than any Pharisaic injunction, and the Sadducees apparently were committed to obeying the Law literally as written, to the letter (instead of the more interpretative and topical Pharisaic approach to it). They were strict in some respects, yes, but compared to other forms of Judaism at the time the Pharisees actually come off as being more lax in a number of areas. Jesus was much more so in some points, though He was also much stricter on others.
The Pharisees were the religious liberals of their time, because they called for a more fluid, grassroots, democratic form of Judaism, one that is not fossilized by time and monopolized by priests and Levites, but one accessible to all and adaptable to various circumstances. Since all of Israel is a “kingdom of priests” as Scripture says, they taught that each and every Jew - not just the priesthood - should thus live and act like one, relating religion to daily life by doing things such as the observance of purification laws (this is why the Pharisees were called ‘strict’). The Law mattered so much that the pious observed it as best they could to please God to the point that they would engage in discussions and debates with each other, so there would be disagreements both within and without.
For the most part though the Pharisees kept these injunctions exclusive to their group and usually never forced them on outsiders (though I think that would not discount the occasional quarrelsome lone nut here and there…

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