It was no surprise that Fortnite on PS4 wouldn't be cross-play enabled with every other version, but something odd is going on with Epic Games accounts. If you've played Fornite on PS4 with your Epic account, you won't be able to use that same account on Switch. The inverse is also happening, limiting accounts that are first used on Switch from playing on PS4.
When booting into the game on Switch with a PS4 account, you'll receive the error message, "This Fortnite account is associated with a platform which does not allow it to operate on Switch." Doing the opposite greets you with, "The Epic Account you tried to link cannot play on this platform." Curiously, this doesn't happen when using an Epic account from Xbox One or PC. Switch seems to be the trigger that makes your account incompatible.
It isn't especially difficult to make a new Epic account, but Fortnite employs a battle pass program that players buy into to receive challenges and rewards. This weird limitation means you could end up losing out on the progress you've made should you accidentally log in to the Switch version while primarily playing on PS4 or vice versa. That really isn't good.
I don't believe this is an intentional bug, but maybe Sony really is playing hardball. At the very least, Epic Games should be addressing the issue in short notice. A lot of fans are angry and you don't want to piss off the massive userbase of Fortnite.