What a great question!
It has been my observation that religion is more or less dead as an influencer of society. It started dying hundreds of years ago, with the rise of the nation-state and democratic politics. Before democracy, power resided in the hands of elites who remained aloof from the people being governed. Religion institutions formed the core of the voice of the people, and fought with states for influence.
But the organizational power of the state and advances in warfare proved to be the end of the old ways of doing things. To field effective armies and navies, the entire population had to work together. The state couldn’t simply take what it wanted anymore, it simply couldn’t organize an entire country’s resources effectively.
Bureaucracies provided a pathway for ordinary subjects to counter the demands of the elite few. The old monarchies couldn’t remain in power unchallenged, and so after a number of revolutions, the nation-state emerged. Subjects / peasants became politically-active citizens. This was the birth of politics as we know it.
Religion, needed as a counter to the depredations of the elites, began a recession into the background. Religion used to utterly dominate the lives of peasants, structuring their societies and deciding how they cooperate. This was the source of their political power and their ability to challenge states. Popes had a huge stick to threaten kings with and that forced them to the table. But with the rise of citizens, religions lost the need and the ability to contend with the state. But until modern times they still held moral authority.
What is challenging their moral authority? Science! In this light, you can look at science as another evolution in the ability of people to determine their own lives. Instead of gleaning insights from old books and old men, people can run their own experiments and work things out for themselves. It’s not perfect of course, science is a human process and subject to error, but just like how it slowly became harder and harder for elites to organize the resources of society, religion simply cannot keep up with science in terms of moral correctness. The Reformation was started when the corruptions of the clergy could not be ignored any more and the Church’s moral authority fragmented.
Science can now take on questions that you used to have to consult tradition for. And so politics, the old system of popular sovereignty through bureaucracy, is running into its limits to keep up with what people want out of life. Science is filling in the gaps.