Ultimately, the inescapable reason there's so much bad press around the exclussivity, and now the huge delay between release dates, isn't the 'evil corporations' paying to keep it off competitors systems, or because MS were deliberately obfuscating the terms of it's 'exclusivity'.
The simple fact of the matter is that Tomb Raider is associated with Playstation and PC. That's where the overwhelming majority of it's fanbase is, and this deal has made that majority salty as fuck, because they're getting incredibly dicked over.
This is why no one gives a shit about SFV, Destiny's DLC, the FFVIIR or any of the other comparable exclussives before and since that no one outside a small minority has ever cared about.
This was a cynical move by SE to take a huge wad of cash in exchange for screwing over most Tomb Raider fans, and by MS to try and force those same fans into buying a brand they usually don't go for.
I mean look at the other current gen Tomb Raider. Lara Croft, Temple of Osiris, received special edition, physical releases on PS4 and PC, but not XO. The reason the games developers gave for it skipping the XO, was that the hardcore Tomb Raider fans that would buy it, aren't on Xbox. There's also the huge split in sales for LC:ToO and TR

E in Playstations favour that bares this out too.
That's ultimately where the bad press comes from. Pissed off fans on PC and especially Playstation. You only need to look at the Tomb Raider forums and fan sites, and social media to see how many of them have been livid about this deal from day one.
MS have not added value to their brand. They've not secured an exclussive that's going to bring in loads of customers that were on the fence. They're just holding to ransom a game that most of it's fans would rather play on different systems, and I can't see it doing MS or the Tomb Raider franchise any good, or being worth the price MS paid for it.
The fact that it's going to release on the same day as Fallout 4 is just adding to what is already a very, very poor decision by SE.
TLDR: There's so much bad press over this because most Tomb Raider fans don't want to play this game on an Xbox. They're salty as fuck. Myself included.