Call of Duty: Modern Warfare 2 MW2 comes with crossplay enabled. However, if you do not want the feature to be active and want to turn off crossplay on your PlayStation, follow these steps:
Starts Call of Duty: Modern Warfare 2
Go to the game settings
Now on "Account & Network"
Now you will find the option "Crossplay". There you can choose whether the feature should be On or Off.
You can also disable crossplay on Xbox. If you want to turn off the feature on the Microsoft console, proceed as follows:
Open your console settings.
Now click on "Online safety and family"
Now go to "Privacy and online safety"
Then click "Xbox Live Privacy"
Select "Show details and customizations"
The menu item "Communication and Multiplayer" then appears
Now there is a tab where you can decide if you want to play with players outside of Xbox Live.
If you want to turn off crossplay, change the setting to "Block"
Now start Call of Duty: Modern Warfare 2. If the change does not take effect immediately, you must restart the game.