I think it's more of a perception problem, where MS was ambiguous about TR's exclusivity until now. With Bloodborne, Sony was upfront about it being exclusive. It feels like, more than anything, people feel betrayed because there was a reasonable expectation for TR to be multiplat. If TR was announced as an MS exclusive when it was revealed at E3, I think there would have been less of an uproar.
The thing is even the reveal is ambiguous. People keep referring to that MS presser as it is the only "official" source of info we have about the game maybe being multi platform. Yet, when you read it, it mentions: "Xbox exclusives shared the stage with blockbusters such as Assassins Creed Unity, Call of Duty: Advanced Warfare, Evolve and Rise of the Tomb Raider, and independent games such as INSIDE, adding to a growing library of games on Xbox One."
The blockbusters they mention, they all have something "exclusive" on XBox One or are being associated to Xbox One. COD has DLC first on Xbox One, Evolve has some deal also about the DLC as well as the beta only on Xbox One, AC is being associated with Xbox One this time around (while Watchdogs and Farcry 4 are associated with PS4) and then we have Tomb Raider which from the trailers, already seemed to be associated to XBox One in the same way AC Unity is.
So maybe there was already some "exclusive" content or deal being made with Microsoft, or maybe the Xbox One was the lead platform (like it is for The Division I believe) and was much further ahead on development on that version. Maybe the PS4 port would have been outsourced, maybe early on there were talks with MS about exclusivity but it was still up in the air at E3? Who knows?
The problem here is everyone assumes, no one has proof, and so people keep bashing MS for no reason IMO, when there might be a lot more that we are not aware of. Maybe some real insider (not CBOAT, but someone from CD who really knows what happened) could actually share some insight at some point or make things more clear. However, franchises move from one console to another, this isn't a first, and it won't be the last. People have to stop the needless bashing, as whether we are talking MS or Sony, this won't be the last we see of this.