Typical “non-industrial” way of getting “milk” is to milk a cow into some bucket/pan to hold the liquid. It will start separating and cream will float to the top. It gets skimmed and used for other products. What’s below is normal milk.
In US (no clue where else), the milk is separated to get ALL fats out first. The the right amounts of fats are recombined with the liquid left over, often fortified with some vitamins and sold as “milk”. This is where you get the exact, perfectly non-separating, homogeneous product, with predictable fat contents.
EDIT: there is also mechanical homogenization process as noted in comment below that does not use chemicals, but instead mechanically breaks down clumps of fats to make them more dissolvable.
Problem is, once you separate the fats and then mix them back in, they don’t exactly want to stay mixed. For this you use stabilizers and other chemicals.
EU apparently is pretty strict on what these “stabilizers” can be, by specific dairy product. US appears to be in an arms race with itself to make these more intricate. These also can be allergens.
Don’t know how wide-spread this is, but I know over a dozen people that are “lactose-intolerant” in US, but can consume dairy quite safely in EU.
A2 could be hitting on something similar, but for some people even non-homogenized milk from the Holsteins (supposedly containing the evil A1) could be the answer.