Here is the JDK 7 String#hashCode(), which operates on characters:
https://github.com/openjdk-mirror/jdk7u-jdk/blob/f4d80957e89....
That's changed in the newer versions, because String has a `byte[]` not a `char[]`, but it was just fine. A hash algorithm can take in bytes, characters, ints, it doesn't matter.
In Java, you don't get access to the bytes that make up a string, to preserve the string's immutability. So for many operations where you might operate on bytes in a lower level language, you end up using characters (unless you're the standard library, and you can finagle access to the bytes), or alternately doing a byte copy of the entire string.
I admit, checksums using characters are a bit weird sounding, but they should also be perfectly well-defined.