A sectarian is a member of a group with a particular set of interests. If you're a religious sectarian, you are loyal to a particular religious sect or group.
Sectarian, as an adjective, describes a member of any political party or religious group that has broken away from a majority to advance their own very specific desires and needs. Sectarian violence, for example, would describe violence that has erupted between conflicting groups or sects. Unfortunately, there are not many places in the world where sectarian strife and conflict do not exist.