A good hash function will provide a near uniform distribution over the key space. This reduces the question to how do I convert a random 32 bit number to a 3 byte RGB space. I see nothing wrong with just taking the low 3 bytes.
int hash = string.getHashCode();
int r = (hash & 0xFF0000) >> 16;
int g = (hash & 0x00FF00) >> 8;
int b = hash & 0x0000FF;