We use it extensively at Verizon, and it exists just fine with 'impure' code, Akka code, or whatever else various teams decide to also pull in. Codebases that don't use Scalaz end up re-inventing it, usually in a more buggy way and at a waste of developer effort.
Reinventing is fine on your own for a learning exercise and I certainly did it a few times, but in production code, just use Scalaz. Or sure, I suppose if you want to use a copy and pasted into a new repo version of Scalaz, go for Cats. I don't even know why Shapeless is brought into the conversation, it has a much more narrow use case and I almost never reach for it.
I've also found the Scalaz community and chat room on IRC quite helpful, whereas I've had some really unpleasant interactions with Cats committers. To go around spreading FUD and promoting an alpha level library that's less than half as popular as Scalaz (according to Github stars) is just irresponsible.