I noticed a lack of God in most public schools. I understand that children come from different backgrounds and belief systems but not having any idea of God present in our schools sets up a mindset of no accountability with our kids. There is no moral compass.
The main reason is what you said. There are too many different backgrounds and belief systems. You can't teach that many different religions and views in school, time would simply not allow for it. That and you have to consider the children. Different belief systems comes with differences that can be views as negative and further cause issues with bullying.
Likely to avoid bullying and and issues between students and parents. Public schools are not funded enough to offer specific classes to include religions either. This is why you will find after school programs for such things. I went to PSR as a child which is an after school class for Catholic beliefs.
In order to offer enough classes for all the varied religions under one school, it would end up costing public schools thousands a month. They can't afford it nor do they have the time for it.
Imagine being a Christian student in a school where it is primarily Islamic or the other way around. Imagine being a gay student where the Islamic religion is taught. There are a lot of problems that can stem from this beyond bullying.
It would cost too much and cause too many issues. They removed the pledge of allegiance from most schools 5 or so years ago because it mentioned God. They want to be neutral as possible.