The extracurriculars offered at a college vary by college, so there isn't necessarily an answer that rings true for all Faith-based colleges, or other colleges for that matter. That said, there are some common types of extracurriculars that are offered by most colleges, Faith-based or not.
Most Faith-based colleges will offer intramural sports or even competitive Athletics (competing with other schools). Intramurals are often student-led and meant for fun. These can be things like soccer, basketball, flag-football, ultimate frisbee, volleyball, and more. Students can sign up and be placed on a team or put together a team, depending on how it's managed, and compete in a tournament style over the course of the semester or however long each sport runs for. If a student joins a university sports team that is competitive with other colleges, the process is different, and the commitment is higher.
Academic extracurriculars and student clubs are also very common at Faith-based colleges. Academic extracurriculars are clubs or groups outside of classes that meet for topics related to study. Sometimes these extracurriculars are limited to students within a particular field of study. For example, a Journalism club or the school newspaper may be limited to students pursuing a journalism, communications, or related degree.
Student clubs are offered for a variety of topics and activities that can be related or unrelated to academics. Foreign language and culture clubs, sewing clubs, theater clubs, music clubs, art clubs, and everything around and in between may be offered at a Faith-based college. Many colleges also allow students to start their own clubs, if one is not available for the activity/subject that they are interested in. The process of starting a club, if you want it registered with the school, is different by college, so students looking to start their own club should inquire with the student life department.
Faith-based colleges, especially, may offer religious or faith-based clubs and extracurriculars. Examples like bible studies, FCA (Fellowship of Christian Athletes), Campus ministries, and worship team/worship clubs are some of the more common faith-based extracurriculars that students may find, but there are others. Some colleges may even offer ministry or community service clubs that give students a chance to practice evangelism and mission work on a smaller scale.
As previously stated, the types of extracurriculars offered will vary from college to college, but these are some of the more common ones that students will likely be able to find at a Faith-based college, or any college. For specifics on what sort of extracurriculars may be offered at a Faith-based college, check the website of the college(s) you are interested in, as many have posted catalogues or lists of their registered extracurriculars and clubs. Otherwise, you may be able to inquire with the student life or admissions departments of these colleges.