Look at the arguments on CC. One of the most common is whether higher ed should be “vocational.” IME–purely anecdotal I admit-- political conservatives tend to think it should be or perhaps a better way to say it would be to say that those holding that view tend to be political conservatives.
With the exception of engineering–a field in which Ivies in the aggregate are less outstanding than in most other fields–and of finance (Wharton) and nursing at UPenn, the Ivies are liberal arts institutions. You’re not going to study accounting, pharmacy, nursing, allied health fields like physical and speech therapy, business and allied fields like marketing, public relations, etc. as an undergrad at an Ivy. I think the absence of these fields of study in and of itself tends to make student bodies less conservative.
I think at almost every college, except perhaps the Protestant Evangelical ones, students majoring in theatre, creative writing, studio art, etc. are more liberal politically. These students make up a higher percentage of students at a college like Brown than at your typical flagship state U.
Look at the posters who are saying it doesn’t hurt–they are in large part people who went to Ivies and top LACs and/or who have kids who did. The posters who are doubting this seem to be those who have no first hand experience with these institutions.