Is Microsoft going to shut down xbox 360 servers?

Eventually.

My guess is probably not soon since backwards compatible 360 games can still access Xbox Live on the XB1 just the same.

Microsoft's top gaming boss Phil Spencer succinctly stated: "Not true." over twitter

Not for a few years at least. Especially not after all that work getting Xbox 360 games working on the Xbox One.

Just like they did with the original Xbox in 2010, they will do it with the 360. It will probably be another 5 or so years before they discontinue XBL for the 360 though.

No

If they do then they're going to lose a lot of money. Not everyone is willing to buy an Xbox One since that thing is more of a money dump than my PS4 Pro that I bought for under $500 with a 3 year warranty and 1tb memory.

They'll just lose money and customers to Sony.