Although I would normally agree with going through the proper channels, ie; teacher first, then principle. In this instance I hesitate.
If it were the case that the child were experiencing some emotional concerns such as anxiety or if his/her needs weren't being addressed, then yes, going directly to the teacher should be done first. After all, the teacher and the parent are the ones that spend the majority of the child's growing years with them.
Although this is not the teachers fault, parental rights have been stripped from public schools, therefore, concerns about personal opinion being indoctrinated needs to be voiced to the principle.
The principle is the "manager" of that school. Their job is to make sure that conduct by both the student and teacher are acceptable, period. The principle makes daily, if not hourly rounds to observe the classrooms and the halls. Going to the principle and addressing this concern will enable the principle to have a "heads up" to a possible problem. A meeting between a principle and a parent should be confidential and I would stress that issue. If the teacher is new, then the principle will be able to help better guide said teacher. That is their job after all.
Teachers "talk" among themselves. They form opinions on personalities, child and parent. Not saying that principles don't, but they are set by a much more strict policy given their responsibilities. (I believe the OP had mentioned about possible recourse by the teacher.) Going in and ranting will always get one labeled, but addressing concerns in a civil manner and expressing what is acceptable and expected is our right as a parent and should be exercised.
Lisa