Is Race relevant?

I saw the following exchange on a feature about black students at Cambridge University on the BBC news this morning:

Student: Do you think this is a place that is institutionally racist?

Vice Chancellor of Cambridge Uni: I think it’s a place where race has not been acknowledged as relevant particularly to the whole intellectual experience of being at Cambridge, so in that sense I would say it is racist because it doesn’t acknowledge race in people’s lives.

This is a massive change that has taken place in the last few years. Previously (say, ten years ago), to view race as a relevant factor in the provision of education, or any other aspect of public life, would, to many people, I think, have been considered racist. Now, though, an institution - and therefore, presumably, an individual person - can be deemed racist by virtue of not taking race into account in its interactions. This complete change of direction is, I suspect, a source of much confusion and misunderstanding in the current conversation around race.
Of course, it can only be a good thing for white people to become more aware of the discrimination and racism suffered by people of colour. But I can't help wondering whether the increased focus on race as a category that defines who a person is - even by those who have never thought of themselves as racist and who previously, at least on a conscious level, considered race to be irrelevant in their dealings with others - might, possibly, prove ultimately to be a cause of increased division rather than a means of healing.