Regarding the effects of an individual teacher's theology and its impact upon student piety, the burden would be upon the institutional authorities--the Board of Governors in policy-making, the headmaster in setting those policies into the context of the school for the other administrators and teachers, and the other administrators and teachers holding one another accountable to the policies and standards codified in rules and institutional norms. Let me try to bring all of that abstraction down into the concrete. One school sees orderliness, respect for teacher, and love for neighbor best expressed in turn taking, so they make a rule requiring students to raise their hands and be called upon by the teacher before speaking. One or another teacher might care more or less for the rule, but institutionally, their duty is to submit to the policy and hold students accountable to it as well. Another school sees orderliness, respect for teacher, and love for neighbor best expressed in free exchange orchestrated by the teacher, so they make a rule requiring teachers to encourage free participation with the expectation that the teacher will ensure all the voices are heard, the lesson follows its plan, and the teacher summarizes the contributions at the end. Again, one or another teacher might prefer the rule or not, but piety will be expressed by everyone seeking to uphold the policy faithfully.
Not all instances of piety reduce to policies and rules, of course, but there are so many of them that do in a school environment that it really is incumbent upon the administration and faculty to work together to be on the same page. At the school where I teach we've often had teachers change their own parenting approach based upon the policies and rules that the school has in place because they could see in their own and other teachers' enforcement that children learned and loved one another better than when left entirely to their own devices.
To go to the original question, I think a lot of what piety looks like in the pre-grammar stages boils down to imitation of order and preferring others: sitting when it is time to sit; standing upright with clothing all in order; looking people in the eye when speaking or being spoken to; responding to commands right away, all the way, and with a good attitude; holding doors for classmates; cleaning up thoroughly and putting things back in the right place; etc., etc., etc.,--AND (here's the kicker), making sure that all of these activities are verbalized in terms of love: "let's love our neighbor by putting everything away neatly so they can find it easily the next time we use it," "We love people by looking them in the eye when listening and speaking," so that the motivation is being encouraged in addition to the behavior itself.