Should I use the pronoun 'my' in the title of an appendix of a thesis?
Appendix A: An Example of My Participation in the Community's Rituals
The use of "I"/"We"/"They" or "My"/"Our"/"Theirs" will be very dependent on the research philosophy that you are working on. I'll give you two opposite examples.
If you are conducting interpretivist/constructivist research, you are acknowledging your role in defining the problems (or things to look at), analyzing and drawing the conclusions. So, using I, my, mine are acceptable and even recommended if you are writing by yourself, which is the case of your thesis.
On the other hand, if you are a positivist, you will try to argue that you had no role in the experiment. You will speak on the third person and try to remove yourself the most you can from the picture.