Regardless of whether we are talking about religion or propaganda, I think his principle should stand. Do you really believe you should be taxed to make sure the Washington Post remains profitable for its owners? Which components do you think Jefferson would support?
Public education even in 1850 is nothing like public education today.
Also, you ignore the debates about the First Amendment itself in Congress. If you read the Annuals of Congress records, it is clear the establishment clause was never intended to go as far as it did today.
I would say it does go slightly further than what some claim, that it only banned a state church. But, it was never intended to go as far as the SCOTUS interprets it today.
It should be noted that for all the talk of that law, Virginia was not exactly following pure separation of church and state even after its adoption.
See Post #17 for more on Jefferson’s interpretation of the significance of “freedom of the press”—in his own words.
I doubt very much that Jefferson would be in favor of FEDERAL control of education, and probably not even of STATE control. I do believe he'd be opposed to his children being forcibly indoctrinated with ideas that he opposes.
I think there was (and still is) a lot of unanimity around the idea that children should be taught to read, to write clearly, to think clearly and to have a solid foundation in facts. I don't think Jefferson would at all been in favor of mandatory public education where they taught the divine right of kings back then, nor of the rights to other folks property and labor being taught now.