I dunno. Moggi 1991 is based on category theory, and, like it or not, is where the treatment of effects in lambda calculi comes from.
That said, the study of lambda calculi is not necessarily category theoretic, nor even is the study of type theory. If we look at type theory through the lens of the Curry-Howard correspondence, we encounter category theory in that the “logic” side is a constructivist logic that is the “internal logic” of an elementary topos, and this can be useful to know.
More to the point, though, it’s category theory—the algebra of composition—that tells us what “composition” even means. So I can’t agree that promoting category theory is unnecessary zealotry, since its absence entails a loss of precision. (I have an intermediate/advanced Scala/cats/cats-effect/http4s interview exercise that hinges on this).
That said, I have dissuaded, and continue to dissuade, functional programmers from “studying category theory to be better functional programmers.” One employer ran a study group on Milewski’s book, and he admitted it didn’t help him with Cats code at all. A Haskell programmer, or Cats programmer, or PureScript programmer, or fp-ts programmer… will learn category theory more effectively than a “Categories for the Working Mathematician” reader will, for the purposes of writing software.