I discovered microg only recently and was instantly very interested but I am a heavy user of Cast so that's a big no for me, though I'll happily jump on it once it's done (if it's possible).
I don't think Cast will be possible as it requires a Google signing cert.
For what's worth I can use Cast (Miracast) without installing Google services. If you would like to get rid of Google services maybe consider buying a Miracast dongle to replace Chromecast?