"... which nobody in society can question without being branded a racist, misogynist, anti-science, cultural appropriator, etc. ..."
If your values are anti-racist, equal opportunity and fact based, then you don't need a "new dogmatic religion" or "an Inquisition".
You just stick to your values and your critics will be judged by their actions.
It sounds like you've had a visit from HR and don't like being accountable for your behaviour.