As we've just detailed, you can turn off Modern Warfare 2 crossplay on Xbox. However, our initial testing has discovered that certain modes do not work with crossplay switched off.
At launch, Modern Warfare 2's big team modes — 'Ground War' & 'Invasion' — do not work when Xbox crossplay is blocked; matchmaking for these modes simply doesn't start. Thankfully, standard 6v6 multiplayer works just fine with no crossplay.