Is Monster Hunter Rise crossplay?

No, Monster Hunter Rise is not crossplay, with no chance to bring across saves between PS5, Xbox, PC or Switch, and that's not likely to change anytime soon. Monster Hunter Rise was originally a Switch exclusive, but time, popularity and success have drawn it across platforms, so now you can play it on more advanced consoles like the PlayStation 5 and Xbox Series X. Unfortunately, progress doesn't carry over between them, and we don't see any likelihood of that changing. We'll discuss the issues of Monster Hunter Rise crossplay and cross-save options below, and if that's likely to change.

Monster Hunter Rise crossplay and cross-save aren't a thing, and probably won't be

As mentioned, Monster Hunter Rise crossplay and cross-save options aren't in any of the platforms, and aren't likely going to be in the future. It's not clear why this won't be a thing, but it's been an issue since the first port, with Capcom simply saying that crossplay and cross-save wouldn't be transferred to PC.

There's no reason to think this is likely to change in the future, as most crossplay games function by having some sort of additional account that the player logs into once in the game (similar to how Call of Duty games have their own Call of Duty account that carries over). 

Considering that Monster Hunter Rise doesn't have an equivalent feature, it's unlikely that it'll be able to implement crossplay any time soon without serious updates - and there's no reason at time of writing to think that'll happen.