If Microsoft is requesting a Xbox Live login for the new Minecraft update, then it's understandable why Sony might be hesitant to allow this. They clearly don't want to advertise for one of their primary competitors.
The suggestion in your second paragraph might be the best way to address this. Rebrand the login as a "Minecraft account", and remove any onscreen reference to"Xbox" branding. They can still use their existing infrastructure on the back end.
There's another complication here, which goes back to what you mentioned in your first paragraph. If the game allows you to purchase cross-platform downloadable content, then which online marketplace does it go through, and who collects the profits? This can open a whole Pandora's box of problems. Consider the following:
Would purchases be handled through PlayStation Store, or a (possibly rebranded) version of Xbox Live?
If the purchase is made on a PS4 console, then would Sony still see a share of the profits, or does it all go to Microsoft?
If the purchase is transacted elsewhere (e.g. an online Web site, a mobile phone, an Xbox One), and the DLC is used on the PS4, then could this be exploited as a vehicle to circumvent PS Store, and thus cut Sony out of any potential profit-sharing? (Imagine a scenario where Microsoft frequently offers "steep discounts" through email blasts, as long as you agree to buy directly from their online Web site.)
If Sony acquiesces to Microsoft's proposal, then could this blow the doors open for other publishers to request similar treatment? For example, I own Rocket League on both PS4 and Steam on my PC. I bought a few DLC packs for the game through the PS Store, but that DLC doesn't carry over to my game on Steam. Could Psyonix ask Sony to open the doors to cross-platform DLC...and if they did, would Valve get angry if I bought my DLC from Sony instead of going through Steam (or vice versa)? If I get a Switch and its version of the game in the future, could I keep buying DLC for that game through PSN and cut Nintendo out of the picture?
These are questions that may not be very easily answered.