Harvard is older than both parties. There is no good reason why it should cater to only one half of Americans.
And it's been a private institution for hundreds of years.
The reason that academia is overwhelming left-leaning is that those are the people that choose to go to grad school and pursue academic careers. For whatever reason (whether ability or inclination) conservatives do so in much smaller numbers. You want conservatives in academia, go get a Ph.D.
If there is a Christian university, it should either be sponsored by Christians only, or similar funding should go to other universities representing other major American groups (for example Jews).
Discrimination based on political views should be treated the same as discrimination based on sexual orientation or race.
Either lose funding, or comparable other universities should be funded so all relevant spectrum is covered.
Federally funded institutions should cater for all Americans. The army, police, schools, hospitals... shouldn't be there only for one half of people.
They did. Remember Trump University? It got shut down for fraud.
If you're looking for an actual conservative university, a better example would be a place like Liberty University. I think the problem is starting an institution is hard, it'll only really hit its stride like 100 years after being founded, and it's hard to keep an ideological project on track for such a long period of time.