I'm a Christian and a feminist. Membership in both groups is a key part of my identity. If you talk to someone with a simplistic understanding of these groups, though, they might be surprised that it's possible to be a member of both groups!
The problem is that we aren't very good at differentiating subgroups that happen to share the same label. We lump Catholics, Pentecostals, and Unitarians into one group called "Christians". We even lump Canadian Christians and American Christians into one group!