It's worth noting that the typical red/blue dichotomy by state is far less useful / accurate than simply dividing between urban = blue and rural = red. both are quite reductive, but you will find yourself far less surprised going by the second than the first.

colleges and universities in particular are a confluence of many demographics that lean blue - they are usually relatively urban, and of course they skew hard towards young and / or educated. These effects are generally far stronger than vague differences such as state borders.

That being said, the main exception to this are smaller schools which are either less urban, or draw far more heavily on in-state / local students. in either case, this would cause the surrounding demographics to have a far greater influence on the overall campus climate