Although Activision and Infinity Ward have not confirmed anything about it, the Call of Duty Modern Warfare Beta seems to perfectly support Cross-Save across platforms, as confirmed by various magazines.
A GameSpot USA editor claims to have used Cross-Save without problems of any kind: ” I played the first beta weekend on PS4 and after downloading the second beta client on Xbox One I discovered I could import my progress, including levels, equipment, emblems and in general all the achievements achieved on the Sony console. “
As mentioned, at present Activision has confirmed the full Cross-Play support for Call of Duty Modern Warfare while it has not been unbalanced with regards to Cross-Save, which seems to be perfectly active and functioning. However, it is not clear if this option will be maintained in the final version or if it is perhaps only a test.
The second beta phase of Call of Duty Modern Warfare is available from 19 to 23 September on PC, PS4 and Xbox One, the full game will arrive on 25 October on all the platforms mentioned.