Bullshit. You can be as conservative as you want as long as you remain silent and not protest anything at all that the diversity and inclusivity mob proposes. One word against that crowd in a SV tech company and you are dead in every sense of the word except physically.
That is the power dynamic of our times and hence why the need for dual personas.
That being said you need to be respectful of everyone, regardless of their religion, ethnicity, gender identification etc. I think it is very possible to do that and still be a strong conservative.