You really don't know what "due process" means, do you? It's a part of legal proceedings, and employment decisions are not legal proceedings.
Due process isn't what prevents school boards from firing teachers. Teachers don't work for the school board, they work for individual schools. Those schools are run by a principal, who ultimately makes the decisions. That principal in turn reports to the district superintendent. That last person is the only one a school board can fire. Teachers are insulated from school boards by two distinct intermediaries. None of the forgoing has anything to do with "due process," at least not in anything remotely resembling a legal sense.