How to decline answering details about my thesis?
The one valid point I can see here(*) for not sharing the state of the thesis:


  For the research, I am visiting classrooms at various public schools.


You should not share the preliminary details of your thesis if this could affect the outcome of your study.
As I understood the question, the school (or some teachers or students) may be the subjects you study, so they should be as little influenced by you as possible (that is, don't tell them that they are in the placebo group).

(*) things would be different e.g. if you were in an engineering field and working towards a patent