Affirmative action will lose because Harvard is guilty. Conservatives will cheer at first because there will be fewer black and hispanic students at their beloved Harvard, but before long they will recoil in horror as the student body's at America's most elite private schools begin to resemble that of UCLA.
If so, they are not true conservatives. Conservatives value individual liberties and equal opportunity, and are against identity politics of all sorts.
Are you upset that NBA's racial composition resembles Africa?
Conservatives do not value individual liberty or equal opportunity, the later of which is literally antithetical to conservatism. To the extent that conservatives do value individual liberty, it's very much in a "freedom of the master" construction.
Conservatism as a political movement began in France in 1790 under the premise that traditional hierarchies (such as hereditary nobility and the clergy) have existed for a very long time so there is probably a good reason for that and the hierarchy should not be changed. Identity - and in particular, the hierarchy of identified groups - is the foundation for all conservative politics.
While Ivy League schools are substantially meritocratic (the number of legacy and athlete admissions is far outweighed by the genuinely brilliant admits) they are also hierarchical in a way that is deeply conservative. The modern divide between these schools is entirely because very few students, professors, and school administrators vote Republican.