Shakugan no Shana, Kyoukai no Rinne Recommendations
Both are supernatural anime with a very normal protagonist who meets someone with red hair who looks human, but isn't. (Well, Rinne is half-human...) Both also involve the red-haired character battling supernatural enemies. Kyoukai no Rinne is more lighthearted, while Shakugan no Shana seems to get more serious.
A character isn't really human, and has some sort of connection to the character who isn't human's world. They both try to defeat evil spirits.