"The constitution doesn't say anything about practicing your religion in a public school. "
Actually it mentions nothing of a public school either.
The Founders would not have approved of the nanny state leftist "public" school system.
They would be aghast at tax money being forcibly taken from citizens to fund a government education system.
We have moved so far from their intent it is laughable.
Your opinion of the current state of the education system isn't sufficient justification for assuming religion should be taught in those schools.
I don't think so.
At the time of the signing of the Constitution, New England governments required tithes collected from all citizens. If you were a member of a government authorized church, then the tithe went there. If you were not, it went to the official government church.
One of the things they did with the money was run schools. Granted, it was done by the church. But the church was the government back then, and this situation continued until about 1820, almost 30 years after the ratification of the First Amendment. The practice wasn't stopped because of an ACLU lawsuit, but because the churches turned over their work to secular governments to avoid conflicts because of doctrinal disputes.
Things have changed, but taking money by force from the citizens to pay for schools was done then, and done now.
I'm not sure that I completely agree with your assessment of what the founders would and would not approved of.
My guess would be that they would not be of one mind on this topic, much as they were not of one mind on almost everything that they discussed.