Hi Peter !
Hmm... long story short:Friction modifiers alter an oil’s coefficient of friction. Typical friction modifiers include organic fatty acids and amides, high molecular weight organic phosphorus and phosphoric acid esters.Perhaps I am conservative regarding automotive oil products, but personally I would not use anything else in BMW cars differentials, than their original stuff(castrol SAF-XJ for limited slip and castrol SAF-XO for regular one)Those lubricant were developped by Castrol in cooperation with BMW for these cars and have special pakage added to its formulation.The reason these differs are loud or whining , because lots of people put in other stuff like Amsoil, Redline, etc...
Peter, remember never ever put 75w90 gear oil to limited slip differ,it calls for 75w140(as original fill) your rear end gonna be much quieter and you will get better performance from it.
BTW do not put any shit (modifiers) into differ , you will only make it worse !