Belief certainly matters in Judaism, and several mitzvos require us to believe certain things. If we don’t believe we should strive to believe, and pray to increase our emunah.
However, the fact is that not everyone is perfect in their emunah, and it is good that we don’t police this. It is much better for an Orthoprax person to be in the frum community, as long as they are not attempting to spread doubt and kefirah to others.
As for teachers, we should ascertain if they are doing a good job. If they are making the children less (rather than more) enthusiastic about Yiddishkeit then they should be replaced, regardless of what their personal beliefs are. That is, let’s focus on results.