You can't be a leftist and support legacy admissions. You can be a right-liberal and support legacy admissions, but even the mildest mild-mild leftism would reject that kind of thing.
If you look at the political tendencies of the elite universities that themselves practice legacy admissions, those tendencies are overwhelmingly to the left of the American political center. I know it’s popular to make a “no true Scotsman” argument against anyone to the right of Mao Zedong but it’s silly.
I think you are failing to distinguish individual elements of the universities you are commenting on. Administration and faculty are very different people. Admin need faculty for prestige, but faculty need admin for funding. Are a majority of prominent faculty members advocating for legacy admissions?
You’re implying that there’s some crypto-right-wing people somewhere in the university and that these people are solely responsible for legacy admissions, but you’re not even willing to state this absurd implication, let alone provide any evidence for it.
I think the thing to understand is that university professors are upper middle class.
They are not particularly aligned with the working class or with leftism. They're usually centrists or liberals.
I think your confusions stems from believing that liberals are the left. Liberals however, are pro-free trade ultra-propertarians. Liberals are to the right of anti-free trade populists.
So by what definition of leftist thought could this possibly be okay?
Wikipedia has one (ideologies that seek social equality and egalitarianism), which this is clearly incompatible with. It's certainly unacceptable to socialists, communists, anarchists, syndicalists or social democrats.
Liberals are not leftists. Liberals are mostly inviolable-property + free-trade type people.
Soviet Russia was not an egalitarian society, it was a brutal dictatorship governed by an effective ruling class of party members. Mainland China is the same. If that’s your standard of “leftism”, you’re drawing the line somewhere to the far left of any self-proclaimed communist party that has ever held power in any country. This is clearly absurd.
You’re the commie version of those annoying right wingers who like to start semantic arguments that the Nazis weren’t really right wing.
Leftism is an incoherent and false ideology fundamentally unsuited to the governance of human societies. Once you recognize that fact, the hypocrisy of actual leftists will cease to surprise you.
Liberals are not leftists. They are not egalitarians and they are not really for social equality.
Allowing universities legacy admissions is a position so far to the right that I don't think any political party anywhere outside of the US propagates for it. There isn't a social democrat in Denmark or something who has vaguely leftist view but who also believes that universities should admit people based on their parents having gone there.
If anyone really favored social equality they would support abolishing the elite universities entirely. Anything short of that still produces an identifiable class of people who attended these institutions, and it’s the existence of that class in the first place rather than its partly hereditary nature that runs counter to social equality.