I've always thought that wool should be able to be crafted into at least 5 string. Also if you dye the wool and turn it into string it should be able to be turned into string of the same color. I don't think colored string should be used on bows. However maybe it can be used on trip wire hook. So if you want to make a bank vault with laser or looking things you can use Red string or whatever.
String is used for tripwire traps, which are meant to be as invisible as possible. Which is why I think gray or black colored strings could work, but nobody's gonna use bright red strings. Best to just uncraft wool of any color into 2 strings, so it's a somewhat efficient way of recycling wool colors you don't use.
Colored strings COULD work against the right blocks depending on how it's colored.
Also, wouldn't it be a tad easier to let string be dyed?