As the title suggests, I’ve just bought a brand new XT M8000 double chainset, which I hope to match with a ten speed setup, comprising of a 11-36 XT cassette and KMC 10 speed chain.

A precursory turn of the pedals whilst fitting resulted in a noisy drivetrain and some reluctance to shift.

Should I swap the chain for an 11 speed Ultegra/XT job?

There isn’t really such a thing as 11 speed chain rings.

If you are using 10 speed everything else then you should have no issues. Keep the 10 speed chain unless its worn

the Sram Red 11spd cranks that came on a C’dale had “10spd” in small letters on the chain ring. AFAIK no difference in rings, just an excuse to sell you a new crank.