Does the "red string" have to do with Kabbalah or Judaism?

No. It is just a myth. I've read from a few Kabbalistic sources- that the color red has some type of effect against Ayin Harah.

So paying $20 for a "red string" isn't worth it, because it's a fake.
If you want something against Ayin Harah, then buy a red rubber band pack for $2.

Rav Perets, is very agianst the color red, and paskens that it should not be worn. This should also be taken into consideration.