It appears that cats-actors is pretty close to being able to be run natively and in scala.js since its minimal dependencies (ie cats-effect) can mostly run on those platforms now.
I did a proof of concept fork here:
https://github.com/Voltir/cats-actors/tree/topic/scala-native-poc
The upstream dependencies are a bit in unstable right now - looks like cats-effect is still working through some issue working with scala-native 0.5.7.
Additionally, scala-futures don't play great in the test code. Instead I used https://github.com/typelevel/cats-effect-testing which seems pretty compatiable with the current tests if you are willing to drop unsafeRunSync calls in favor of the extra test dependency. But with a few minor other changes, I was able to get the first couple of AskSpec tests to run natively, which is pretty cool :)