Isn't the word ethnicity a convenient - if not totally scientifically supportable - way of describing groups of people who have different physical characteristics and possibly different attitudes, religions and customs?
I get the point that in reality ethnicity is, to some extent, a social construct. Some people - white and non-white - object to completing the ethnicity questions in certain documents, possibly for different reasons. Some white people feel the questions, aside from being intrusive, are unnecessary. Some non-white people also feel they are intrusive and that they reinforce the notion of intrinsic differences between various groups of people.
Of course, we are all human beings and should be treated with equal care and respect. In reality, though, there is enough evidence now to demonstrate that certain groups are discriminated against. If we throw out the ethnicity classification - even if, technically speaking, it may not scientifically accurate, then aren't we also throwing out the one way in which monitoring of access to services can be carried out? In France, for instance, there is no monitoring of ethnicity in relation to access to health, jobs, employment, etc., etc., and several commentators feel that this makes the discriminatory practices faced by certain groups impossible to quantify or address.