According to this source hydrophobic behaviour occurs when a molecule does not have a charge or is neutral and therefore cannot be attracted to the negative nor positive parts of water. Casein has an isoelectric point of 4.6 and milk has a pH of about 6.7. As a result, the casein proteins would have a negative charge, hence wouldn't the casein be attracted to the positive part of water?
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In milk, casein exists as a colloidal aggregate (casein micelle) with the properties you state, but purified casein is different. It is rich in proline (shown below), has no disulfide bridges, and hence little tertiary structure to hide the hydrophobic residues in the core of the protein with the hydrophilic residues on the surface to bind to water. In addition to having a hydrophobic side chain, proline stiffens the aminoacid backbone, hindering tertiary structure. The net effect is a molecule with too much exposed hydrophobicity to be water soluble. Casein micelles are complex structures and quite different from lipid micelles.
PROLINE 
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$\begingroup$ Why does a lack of tertiary structure result in hydrophobic behaviour? $\endgroup$– LiamCommented Apr 22, 2019 at 21:36
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$\begingroup$ Folding can allow a protein to segregate hydrophobic residues in the core and hydrophilic resides on the surface. $\endgroup$– LuquettmCommented Apr 23, 2019 at 15:00