Anyone who has spent any time at an Ivy League university (or anything like it) knows that it’s ludicrous to think that a student would be rejected for being an engaged, thoughtful conservative. The student bodies at all of them lean liberal, but every elite college has decent representation of vocal, active conservatives. Generally, the spirit of those colleges is that active, engaged anything is better than bland, as long as the student seems thoughtful and independent-minded, and within the mainstream of post-Enlightenment intellectual traditions.
If someone were a Biblical literalist, that could be a problem, unless he or she clearly demonstrated that he or she was prepared to live in and engage with a world that does not regard the Bible as the fundamental source of non-metaphoric truth. If someone were the type of conservative who believes that some races are superior to others, or that homosexuality is evil, and those were the issues he or she chose to engage with most – that would be a huge red flag for admissions. But there are plenty of kids on elite college campuses who believe in limiting government, especially the federal one, who hope someday to have a job in a Paul Ryan (or Rand Paul) administration, and who gleefully quote The Fountainhead to one another. Most (not all) arrived at college that way. If admissions teams were trying to keep them out, they are failing miserably.
The most recent Pew data show that the more education people have, the larger the percentage of them who identify as liberals. The larger percentage of them who identify as conservatives, too, as opposed to nothing, through the population with college degrees (although the liberal cohort outnumbers the conservative cohort in every group with high school degrees or more education than that). When you get to people with graduate and professional degrees, however, the percentage of conservatives takes a meaningful dip, while the percentage of liberals increases over just BAs.
Anyway, the population of students at elite colleges is a population of students who will overwhelmingly be getting graduate degrees. Their political self-identification basically tracks that of the population cohort which they expect to (and will) join.