I won’t tell someone where I work and live or anything else personally identifying, but ideas and values? Totally open on that.

As for not caring what people think. You might be getting hung up on the definition of “care.” I think we all care, to a greater or lesser extent, about things we profess to not care about. Speaking specifically for myself, I might seem to care to some extent, but I don’t let what others say or do affect who I am. That’s an important line to draw, and to recognise when it’s being approached and to disengage when it gets pushed, but learning to do so comes with age and experience.