Is it safe for transmission and rear differential if you put staggered rims on 2012 Jaguar XF 5.0 profolio RWD x250 non super charger ?

 

Yes. But you will need to get the right wheel width and offset so it doesn't cause tyre rubbing issues. Note that the staggered wheels off the XFR and SC models won't work as I believe their rear axles have wheels with a very different offset from the non SC models

 

I don't think that is the case, I put after-market staggered wheels on my old XFS (3.0 diesel with non-staggered 18" wheels stock) and had zero problems, and then when I sold the XFS and bought an XFR I transferred those wheels over to the XFR and again had zero problems. AFAIK there is no difference between the suspension set-up on the 5.0 Portfolio and the XFR/SC other than the XFR having 5 mm lower springs.
The wheels I had were Coventry Whitley 10" x 20 and 8.5" x 20 and the tyres were XFR spec 285/30ZR20 and 255/35ZR20, I can't remember the exact offsets but the fronts were the same as stock (+45??) and the rears were +49 I think.
Thing is the stock XFR rear wheels have a massive +66 offset which tucks them waaaaaay in so there is oodles of room to push them out a fair bit with less offset.