Since I talk to anyone anywhere no matter how dressed, I am not sure what I have or have not said to strangers before. I would guess that while in male mode, I probably have not unless the topic was about drag queens or some other "T" related topic. In female mode, it is fairly obvious what my roots are and I know that I have told many strangers, some of whom didn't realize it until I told them, males and females. But that is not too common.
I do understand the need to share and the truth in telling a stranger something when you will never see them again, probably! I am a good conversationalist with strangers and many have told me some of their secrets that not many others had known. We all tend to need to share some special things about ourselves every once in awhile. We just need to learn when and who will respect what we tell them.