TM7, the Ummah is akin to the Talmud, yes. It is wisdom from the community of Islam. Comparatively, they would be stronger than apocryphal texts, but not as authoritative as the Quran. The Sharia is not built on the Quran directly, but on all 3 stacked - Q, H, U, S. Imagine the Pharisaical legal system during Christ, where divorce was granted for burnt toast. Christ's reply, it was not always so, God hates divorce, Moses granted because your hearts were hard (like Pharoah). That's sharia today.
Puritans were in colonial charter, under appropriate authority and were law abiding. In the main they practiced personal piety, leaving public piety to the courts. There were exceptions to this rule, which were condemned from the pulpit citing canon.
In the OPs example you have an unlawful community, operating outside of legal charter, enforcing a public piety standard on persons not subject to said standard, on the basis of opinion not canon. Regardless of motivation, it's wrong, and does not compare to the Puritans.
There is a vocal minority of Christians in the US who are also dismayed by degrading public morality. They too use the tool of interpretation over exposition to support their views. They have however stayed within the legal system, exercising their rights. And when they stepped outside of the law, they became criminals (Romans 13).
The devil is in the details, the differences between the OP and the comparisons are huge.
