Historically, Christianity scholars drew a distinction between the sacred and secular. Christian scholars saw the sacred as being above and more important than the secular.
The drive for a separation between church and state came from the religious community.
In contrast, of course, the political class tends to see religion as a means to control the people. The drive to mix church and state usually comes from the political class.
Sadly, the modern world is full of religious leaders who seek political power and state authorities who want to take control of the beliefs and spiritual lives of the people.
So many people see the tax-exempt status of churches in the US and think, "why isn't government plundering that, too?" instead of, "Why are we allowing the State to rob anyone?" I was just listening to a podcast about the history of Columbus and how he turned to what was effectively taxation of the natives as his first scheme to plunder all the gold he could. But people can't call that taxation because it would require them to rethink what they accept in today's status quo. And of course the flip side of "the state needs to control religion" is the loony anti-library movement in the new Trans Scare echoing the Satanic Panic over rock music and backmasking from the 1980s.