Hunt: Showdown may well get crossplay sometime down the line, but if you were hoping for any sort of concrete information on this exotic feature, Crytek is almost entirely mum on the matter.
The matter of introducing crossplay into the equation has recently been brought up in an interview, though it's clear that Crytek doesn't want to lean either way just yet.
Crossplay in Hunt: Showdown?
"We're still investigating options," said Crytek in their latest interview, speaking tentatively on the matter of crossplay. "We’d like to offer cross-play at some point but it all has to make sense of course."
If we'd want to be cynical about this statement, we could simply assume that this is a political response designed to neither confirm nor deny the idea of crossplay. Having said that, an earlier question about Hunt: Showdown getting an enhanced console release on PS4 PRO and XBONE X does give us further insight in the matter: "The main improvements will be regarding resolution and shader quality. The framerate will still be locked to 30fps though, as we estimate that letting some players reaching higher framerates would be an unfair advantage in such a highly competitive game."
This tells us that it is very unlikely that the PC version of the game will get crossplay with consoles, for as long as Crytek wishes for the playing field to be equal in this regard. We'll see how things go, though.