Religion I think is slightly different in some ways since methods can be found to allow different religions to co-exist - you gave an example of people choosing which day of the week to take off.

But ethnicity is different, so is gender and disability, and also age, because prejudices and stereotypes exist that marginalise those groups.  

If no data is collected then this cannot be monitored for patterns to emerge. eg very, very few women are Chief execs compared to men.  Is this because women are lazy, or because they have chosen to take time off for children or because they choose to paint their nails and dress up instead of working hard?  Or are there other factors that are causing disadvantage and preventing women from reaching senior positions?  We can only look into these trends when we have the data to show that there is some anomaly. Same thing applies to ethnicity but the causes are much more subtle.

If men and women, and black people and white people are so equal - why are there such big differences in outcomes?

I'm intrigued as to why the British approach is to gather data and find out more about why and how differences occur and the French approach is to treat everyone the same and not monitor anything.

Ad astra per aspera