Different tax coffers, and besides, the "drug war" and public education both have the same goals: supplication to the State.
The Montessori schools are all private as far as I know. Their educational philosophy is not at all inconsistent with conservatism and there are plenty of homeschoolers using Montessori materials.
Back on topic, a great teachable moment was missed here. If only the teacher had asked in the presence of the kids to see a warrant, and not seeing one, had closed and locked the door, turned back to her class, and resumed the lesson.