includes language regarding the separation of church and state. Not very specific language, but language nevertheless.
The problem is that Christianity is clearly the dominant religion in this country. What that means is that there is a majority that adheres to that religion. That's a problem in a democratic system, since the majority can pass laws. The constitutional language is not specific enough, though, to ensure that displays of religion in government owned places and venues are not allowed. So, there's always a risk that a majority of some kind will push for such displays.
It took a very long time to get specifically religious prayers out of places like schools and government meetings. In fact, that was never 100% achieved. The words "under God" got inserted in our previously non-religious pledge of allegiance that way. That happened in the 1950s. Before then, it was not there. I learned it without the reference to a deity.
We eventually came to understand the first amendment to prohibit the government from having anything to do with religious worship, but the language remains unclear, so we have to fight that battle again and again. Now, we have a SCOTUS that seems ready to allow religious practices within government-sponsored events. We'll have to fight the battle again, it seems.