Chilled or shelf stable beverage products which are physically stable, visually opaque and do not precipitate over time are disclosed. These products contain from about 5 to about 99.8 % milk, from about 0.05 to about 0.8 % of a food stabilizer and a food acid. The first step of the process involves mixing milk with a food stabilizer under high shear mixing conditions to form protein/stabilizer particles having a median particle size of less than about 0.8 microns. Then, while still maintaining the particle size of the protein/stabilizer particles at less than about 0.8 microns, the protein/stabilizer mixture is acidified to a pH ranging from about 3.2 to about 4.5. In order to maintain the requisite particle size of the protein/stabilizer particles during the acidification step, the protein/stabilizer mixture is maintained under high shear mixing conditions at a temperature ranging from about 4 to about 30 DEG C.