Thomas Jefferson was writing a letter that had absolutely nothing to do with the first amendment.
Also, Thomas Jefferson was in France at the time the first amendment was made. So this separation of church and state is hardly debatable as the meaning of the first amendment as Thomas was on the other side of the world when it was written.
If the author meant to have separation of church and state, he would have written it so. If he really believed that religion needed to be out of the school system, then he wouldn't have said and believed that he felt the bible should be the principal book used in public schools.
The separation of church and state nonsense was created by activist judges who are basically making up their own constitution.
If people want to have their kids study at a school that is devoid of religion, then by all means go to one. Or begin one. That's what this country is all about.