We have equal opps monitoring forms for various reasons - always anonymous and purely to measure the stats rather than to identify individuals as being one thing or another.

No idea if parents are asked to identify their child's ethnicity for schools in the UK.

With recruitment the monitoring forms gives an idea of the numbers of people from different groups who apply and who get appointed in an organisation.  So it helps to highlight whether they are getting no applications from ethnic minorities or if they get a high number of applications from women but no women are getting appointed. Therefore the organisation needs to make changes to be more inclusive or to address any causes for there being a poor diversity of applicants or appointees.  

The only thing that isn't anonymous is when a candidate chooses to declare a disability in order to request adjustments for the interview process eg wheelchair access or a loop system or large print information.

For events we run at work it is important to ensure that we are getting a good diversity of attendees since we run events for representatives.  So we want more people from under-represented groups to come along because they are a direct link to people in workplaces.  So we measure diversity so that we can monitor whether we are being successful in encouraging more people than the usual suspects to come to our events.  All of the information is anonymous and is used without reference to individuals and just shows us a picture that we can measure our progress by.