According to Karol Severin, lead analyst for game research at MIDiA Research, Sony can and should block any attempts at cross-play coming from Xbox One. This is because Sony and PlayStation 4 have incomparably less to gain from cross-play.
Severin claims that PlayStation 4 wouldn't benefit from cross-play because Sony own the vast majority of the console market which itself isn't growing anymore. According to Severin, current focus of either side of the console cross-play conflict is to grab the competitor's users for themselves.
Considering Sony's massive cut in the console market cake, it is only logical that Microsoft would attempt to grab a slice for themselves. Or at the very least, Microsoft might want to use Sony's slice of cake to make their own tastier. This would be made possible by merging online lobbies, as PlayStation 4's huge player pool would mean shorter queue times for Xbox One users and in turn, overall better user experience. PlayStation 4 on the other hand, would just lose the competitive advantage by allowing cross-play.
There is also the fact that many players have built up friend lists on PSN over the years, which is one of the reasons why not many players might want to switch to Xbox systems in light of Sony's apparent villainy, on top of PS4's exclusives such as The Last of Us and Uncharted that keep growing the console's fan base.
Now, the integrity of MIDiA research could be called into question as Sony is one of their clients , while Microsoft is not, which could damage their objectivity. On the other hand, the facts about market share they presented have been confirmed by other sources and their views are valid. For example, not letting your competition catch up is definitely good business, although it may not be entirely ethical as Sony also cripple their users' Fortnite accounts.
Then again, Microsoft are apparently taking moral high ground by posing as the saviour knights of cross-play, even though it was them who denied cross-play attempts in the past. In hindsight, their jab at Sony via tweet about playing Fortnite with Nintendo seems rather duplicitous.
PlayStation has definitely built a massive user base over the years through hardware and exclusives that drew players in, but their PR could use some work. Their weak response to the cross-play backlash could have been easily averted if they outright stated they have enough players in their network, which is about 80 million, and therefore did not need to expand.
Bottom line is, both Sony and Microsoft are making good business moves, although questionably ethical from both parties, and may ultimately become detrimental for players. Sony is doing this by preventing Microsoft's growth in the console market and the latter by degrading the competitor's public image. Sony's ethics are called into question since they are basically holding Fortnite accounts hostage, and Microsoft's ethics are gone along with their integrity after shooting down previous cross-play attempts.
To top it off, Fortnite Battle Royale is actually free to play on PlayStation 4 just like it is on PC, where the game originated. This means you don't need PS Plus in order to play the game. Meanwhile, you have to subscribe to Xbox Live Gold so Microsoft are also holding your Fortnite hostage if you don't pay their monthly 10 bucks troll toll.
In the end, both Sony and Microsoft have adopted anti-consumer stances by making their users suffer the collateral damage of their corporate warfare. Players who registered their Fortnite accounts with PS4 can not use them on Switch or Xbox One and Microsoft's users have to pay to play a free game.
Evidently neither company wants to alienate their customers since a happy customer is a loyal customer. They are both pulling moves opposite to customers' well being though, since it seems that running your competitors into the ground is several floors higher than keeping consumer base happy on the corporate pyramid of priorities.