In Texas, part of your question is already defined. Most school districts have moral turpitude clauses that give the school district the authority to terminate the employment of a teacher whose actions outside of school tarnish the reputation of the employee, campus, or district in a negative way. While there isn't a list outlining moral turpitude, it usually includes "dishonesty, violence against the weak, and sexual depravity", but it must be interpreted on a case by case basis.
As for assignments with an agenda, it would be difficult to prosecute the teacher unless the agenda was criminal or discriminatory. With that being said, parent complaints against such assignments usually effect a change if presented to the principal, superintendent, or school board.