Would it be illegal to put different oil in a diff? I'm not so sure about that. It would just be a "competitive advantage" that you might not want to share.
Now, if you had to physically modify the diff to change the oil, like drilling a drain hole or something... that would be illegal modification. But if you could change the oil without altering the parts, why not?
What next, are they going to start checking oil viscosity? "It's 85 degrees today, your owners manual specifies..." I don't think so.
