A large part of the domesticated animals bred in e.g. Norway (because I happen to be from there, not for any particular other reason) are bred largely independent of the agriculture.
Goats and sheep have been popular in Norway for a long time exactly because you don't need to provide food for them from a field you tended, but can send them out to graze in untended fields or in particular up in the mountains during the summer, and can if you don't have access to hay from a farm, collect hay/grass from untended fields to serve through winter. While there's certainly benefits to combining the two in climates like Norway where you need to collect a substantial food source for winter, even in Norway that was/is a convenience rather than a pre-requisite.
Up North, the Saami people have been nomadic for as long as we have recorded history of them, without any agricultural tradition, and some communities eventually took up herding and taming reindeer while continuing their nomadic lifestyle, following the migrations of the herds, in large part because while there's copious food for the reindeer, the soil and climate is not conducive to agriculture. They've largely done this without any nearby source of hay or other food from agriculture available at all.
Whether or not there's historical basis for saying agriculture came first or not, I don't know, but there are plenty of examples that shows that agriculture isn't required for domestication.
First you make something. They you make it good. These days we call it "minimum viable product (MVP)".
Get a bottle of fat milk straight from a cow, leave it on the kitchen table for a couple of days to turn sour (depends on room temperature) and you'll get yogurt, maybe not as thick as the one you can buy at a store, but it's good nonetheless. Then if the batch was good, you can save some of this batch for later batches, for an addition of bacteria cultures, thus with each successive batch you'll get better and better results. There are absolutely no additives needed (unless you make a business out of it, in which case you want predictable results), with the end-result being 100% chemicals free.
Now try doing that with the bottled milk you can find in the stores.
EDIT (reformulated):
So, consumer tastes are changing based on industry trends ... like these fuckers put extra sugar in everything, being a vicious cycle, because extra sugars in foods give dependency on foods with extra sugars in them. And let's not forget of additives like gels for extra-thickness, or dyes, or powder milk, or other chemicals (because degreased milk or yogurt does not resemble real milk or yogurt, so they have to make up for it somehow) and also preservatives for longer shelf life, etc, etc...
Many consumers would turn their nose on real, fat, non-pasteurized milk or on fat barbecued pork neck, because it's somehow unhealthier than McDonalds' burgers or diary products enriched with chemicals.
And tastes are grown, so if people get used to Danone yogurts that never rot, then that's what they start expecting.
Funny story, the punch line for a Danone milk cream in my country on a TV commercial has been "look how well it dissolves". And I was like "oh wow, can cream really do that?". Go figure.
I truly doubt that.
"Chemicals" when used in the context of food, means "artificial food additives".
You may disagree that such additives are bad for you health - but just how our early ancestors had low-lactose tolerance, we also have low tolerance for such additives. Maybe our children's children will be able to digest such foods better / more efficiently and without side-effects, but in the meantime there's a wealth of research showing strong links between food additives and increasing rates of cancer, obesity and diabetes.
I don't think sequence is quite right. There are several non-agrarian nomadic peoples that raise large land mammals for their milk. Keeping it in the cow/horse/camel keeps it from spoiling.
Cheese and butter just makes it easier to transport the energy without having to transport the cow.
(fermenting it also gives it longevity and was known in much of the ancient world)
You may not get to creating Emmenthal/Parmesan straight away, but there are many other viable steps prior to modern cheese.
Indeed, Norwegian goat cheese is a whey cheese, made by boiling milk, cream and whey leftover from other production (such as more usual casein based cheese). There are a number of other traditional whey cheeses from other countries as well.
Lactose :)
Bacterias split lactose to grow, consuming energy in the process and dissipating it as heat and runaway gases.