The overarching answer is no. Generally, a student does not have to identify as a Christian in order to attend a Christian College. Some Christian Universities will ask for a personal testimony as part of their application process, however that does not mean that you will be rejected if your testimony does not end with you proclaiming yourself to be a Christian.
There are some Christian Colleges that will require students to be Christian, and they are the exception to the majority. Most Christian Colleges will allow non-Christians to attend, however the expectations for conduct and curriculum do not change for them. Non-Christian students attending a Christian University will still be expected to adhere to the student handbook, which will most likely be based on biblical morality, even if the student does not necessarily agree with the values. Additionally, if the University requires bible classes, a minor in theology/bible, or attendance at chapels, non-Christian students will not be exempt from participation.