The General Crisis of the 17th Century

The ideas encoded in the agreement are basically the reason we think of events like the Crimean secession[1] as an unconstitutional Russian annexation regardless of whether it happened by a public vote or not: even if there was a referendum and even if that referendum was formally valid and the outcome was in favour of the secession, the constitution of the Ukraine forbids the secession and therefore renders the referendum invalid by definition.

It's also important to note that these ideas of statehood popped up in the (at the time) Christian world and therefore strongly shaped the face of modern Christianity and the separation of state and church in the West (which even in its worst cases still works better today than it did before the Enlightenment). This didn't happen in the Islamic world, at least not in the same way (though there are examples for church-state separation as in post-WW1 Turkey). I think this provides some insights into why that part of the world's politics is so poorly understood by Westerners (e.g. consider the tribal politics in Afghanistan or the Sunni-Shia conflicts all over the map).

[0]: https://en.wikipedia.org/wiki/Peace_of_Westphalia

[1]: Whether it was an annexation or secession and whether it was formally valid or not is a separate debate. There is a lot of evidence indicating that it was, to say the least, influenced by Russia, which would have made its validity doubtful even if it wasn't unconstitutional.

For instance the lot of many faiths in the UK started improving with the toleration act of 1668. Why were Catholics excluded? Because there had been actual attempts to kill English kings (most famously the Gunpowder plot) and the Pope kept the stance that Catholics should try to overthrow England's government. The Catholic church maintained that position until 1766. In response, England started treating Catholics better. First in various colonies, and then for England itself with the 1778 Papists Act. Something much closer to equality arrived as you noted in 1829.

Atheists got worse treatment. For example they could not testify in UK courts until 1870. And even though atheist Charles Bradlaugh started getting regularly elected in 1880, and he was not allowed to be a member of the House of Commons until 1886.

The US was fundamentally no better, and in practice worse despite the Bill of Rights. For example it was not until 1961 that the Supreme Court ruled that atheists could not be barred by their non-belief from things like being a notary public.

But for all that we can legitimately criticize about the way these ideas were put in practice, they are worlds better than when Henry VIII took land from Catholics for not recognizing his marriage, his daughter Mary killed Protestants for not recognizing the Pope, the Pope in return tried to convince Catholics to try to kill Elizabeth I, and James 1. Both then passed various laws penalizing Catholics in retaliation.

Remember the Bloody Question? "If the Pope should invade England, which would you support? The Queen or the Pope?" Killing people who said, "the Pope" was pretty brutal, but reflected political reality.

This is called "historiography", and were it more commonly taught in US primary and secondary schools, fewer Americans would think of "history" as being dull -- an endless stream of bare facts lacking context is indeed dull as dishwater; it's in the drawing and analysis of narrative that all the interest lies.