To give some ideas of Puritanism (just learned about this word and movement, thanks by the way) form a the perceptional side and the origin of the word as it is used.
There were substantial works of theology written by Puritans, such as the Medulla Theologiae of William Ames, but there is no theology that is distinctive of Puritans. "Puritan theology" makes sense only as certain parts of Reformed theology, i.e. the legacy in theological terms of Calvinism, as it was expounded by Puritan preachers (often known as lecturers), and applied in the lives of Puritans.
In the relation of churches to civil power, Puritans believed that secular governors are accountable to God to protect and reward virtue, including "true religion", and to punish wrongdoers. They opposed the supremacy of the monarch in the church (Erastianism), and argued that the only head of the Church in heaven or earth is Christ.
The idea of personal Biblical interpretation, while central to Puritan beliefs, was shared with most Protestants in general. Puritans sought both individual and corporate conformity to the teaching of the Bible, with moral purity pursued both down to the smallest detail as well as ecclesiastical purity to the highest level. They believed that man existed for the glory of God; that his first concern in life was to do God's will and so to receive future happiness.
Like some of Reformed churches on the European continent, Puritan reforms were typified by a minimum of ritual and decoration and by an unambiguous emphasis on preaching. Calvinists generally believed that the worship in the church ought to be strictly regulated by what is commanded in the Bible (the regulative principle of worship), and condemned as idolatry many current practices, regardless of antiquity or widespread adoption among Christians, against opponents who defended tradition. Simplicity in worship led to the exclusion of pre-Reformation vestments, images, candles, etc. Puritans did not celebrate traditional holidays e.g. Christmas which they believed to be in violation of the regulative principles.
Some strong religious views common to Puritans had direct impacts on culture. .......
Social consequences and family life
Puritan culture emphasized the need for self-examination and the strict accounting for one’s feelings as well as one’s deeds. This was the centre of evangelical experience, which women in turn placed at the heart of their work to sustain family life. The words of the Bible, as they interpreted them, were the origin of many Puritan cultural ideals, especially regarding the roles of men and women in the community. While both sexes carried the stain of original sin, for a girl, original sin suggested more than the roster of Puritan character flaws. Eve’s corruption, in Puritan eyes, extended to all women, and justified marginalizing them within churches' hierarchical structures . An example is the different ways that men and women were made to express their conversion experiences. For full membership, the Puritan church insisted not only that its congregants lead godly lives and exhibit a clear understanding of the main tenets of their Christian faith, but they also must demonstrate that they had experienced true evidence of the workings of God’s grace in their souls. Only those who gave a convincing account of such a conversion could be admitted to full church membership. While women were typically not permitted to speak in church, they were allowed to engage in religious discussions outside it, and they could narrate their conversions......
Please try to oversee the aspects in regarding of God but maybe replace it with Dhamma and Vinaya or other other objects of right view. And prayers are maybe good replaced by samadhi and panna.
If we look on some of this ideas, it is very similar to the main effort of leading western Buddhists today (especial in the Theravada seciton), which also focus on the message and are not much attached to ritulaes and hirachies which are well established and enrooted in traditional countries. Maybe to much.
When we look for example to outstanding people like those who have founded the today Thai-foresttradition (kammathana) we might see similar tendencies.
The striving for purity is twofold and beginns of cause with the own mind. The Dhamma-Vinaya also puts much effort in maintaining the Sangha (body) pure. Of cause there is also a risk of "extremism" if things are taken to literary without doing in accordiance as well as it easily gives rise to pride or a shelter for self-importance.
How ever, puritanism is never a mainstream thing and if it grows to a bigger movement it is mostly extrem negative. But it is how every a striving which is often mentioned by the Buddha, starting with one self and give a helping hand to those who are near and able to take a hand.
So to clean the word puritanism a little from its negative inspiration needs much focus on one self and the constant remembering how easy things grow to extrems if not understood at all in its root. I guess we can steal from every "ism" as long as we do not addopt the negative side.
So does the Puritanism needs some Puritanism?
And what does have to do with your self?
(ps: should be lesser a talk about other sects)