Why does Ammonium sulfate cause proteins to precipitate?
Well, I wouldn't know how to sum it up better than chemwiki.ucdavis:


  To achieve this conformation the molecule folds in such a way that all of the hydrophobic parts of a molecule are aggregated together and the hydrophillic groups are left to interact with the water. In the case of proteins it is the charged amino acids that allow selective salting out to occur. Charged and polar amino acids such as glutamate, lysine, and tyrosine require water molecules to surround them to remain dissolved. In an aqueous environment with a high ionic strength, the water molecules surround the charges of the ions and proteins. At a certain ionic strength, the water molecules are no longer able to support the charges of both the ions and the proteins. The result is the precipitation of the least soluble solute, such as proteins and large organic molecules.


If you ask what the aminoacid content of bovine serum albumin is, I'll cite:


  Glycine,
  illanine,
  Valine,
  Leucine,
  Isoleucineh,
  Proline,
  Phenylalanine,
  Tyrosine,
  Tryptophan,
  Serine,
  Threonine,
  Half-cystinee,
  Methionine,
  Arginine,
  Histidine,
  Lysine,
  Aspartic acid and
  Glutamic acid. Source