In a blog post, Sony say:
Following a comprehensive evaluation process, SIE has identified a path toward supporting cross-platform features for select third party content. We recognize that PS4 players have been eagerly awaiting an update, and we appreciate the community’s continued patience as we have navigated through this issue to find a solution, Kotaku reported.
That path begins today, with an open beta for Fortnite that’ll let PS4 players go up against people on the Xbox One, Switch, PC, Mac and mobile.
In perhaps an admission as to why this has taken so long, when the competition has allowed it for ages, Sony adds that “This represents a major policy change for SIE”, and say there’ll be more information on “other titles going forward” when “we have more details to share”.
It would make sense that it’s been a policy challenge rather than a technical one, since cross-play between PS4 and Xbox One was accidentally turned on last year before being quickly disabled.