Sister Sledge -- We Are Not Family ... For the Pope

The Pope may have issues with one of the sisters ... from Sister Sledge. We're told the group -- which is scheduled to perform for the Pontiff Saturday -- is refusing to include one of its members, and she's not going without a fight.

Kathy Sledge has been told by her sisters she cannot participate in the show. It's unclear what triggered this particular feud, but there's been long-standing tension between Kathy and the rest of the group.

Kathy says she's tried to reconcile with her sisters ... but to no avail.

We're told Kathy is not taking this lying down ... she's planning to get onstage someway, somehow when the group performs at the World Meeting of Families in Philly.

Everyone can see they're not together.