I think the game is more focused on survival as opposed to the villagers' personal spirituality. People adapt with their environment and situations and through their more spiritual actions they're adapting to their new home. One of the key survival tactics is to explore the area and learn as much as you can so you can to do this adaptation.

I live in a Christian community although I am not Christian but sometimes I find myself having to partake in the activities anyway in respect of my friends and community. This is different for everyone of course, just a little example

We, as the guiding hands of our villagers, are helping them survive and satisfy their curiosity of their new home. They are given the tools of the villagers of the past to survive and our villagers choose to honor their hard work and livelihood. Perhaps this island needs that level of spirituality for the villagers to survive, although the puzzles hint that it's just a part of discovering the island's history.

I respect everyone's belief systems and traditions and even partake in them without being part of that religion myself, this is what I see in our little villagers. The island was once someone else's home and I would restore it and respect the area as I would my own home. This is where the clever use of the word "honor" appears instead of "worship".

I would find it disrespectful if our villagers removed the ruins and built different things to make it more religion-specific. Just imagine if that rock was carved into a specific religious figure I would've had an issue with the game if that happened!