Hmm. Well, the technology itself isn't complicated-- even Dresden couldn't hex it up. As Quantus points out, it's the knowledge of biochem that's a sticking point. I could suspend my disbelief for it though: ancient peoples couldn't tell you the reactions that made grain-water into alcohol or made milk into curds, but that didn't stop them from making beer or cheese! Maybe the people who run the vatteries don't know exactly what is going on, in the biological or chemical sense, but they do know what they have to do to produce something edible? That covers a lack of scientific (rather than practical) knowledge of the process...
To Artish's point, Alcohol mostly comes about by letting fruit juices and such spoil, and the secret to all cheese in history is cooking the stomachs of baby mammals (requires an enzyme from before they switch to solid food) which i imagine happened pretty often when they threw all the scraps into a stew-pot and notice that the cream soup stock has gone all chunky. I could see something similar happening to make a homogeneous tofu-style protein paste, scrounging whatever scrap animal matter they could and rendering them down into Pink Slime.
But to go to all the effort to artificially sculpt realistic animal tissues for what would be essentially a cosmetic "texture" difference seems a stretch to me. Especially if animals are rare enough that they arent typically raised and slaughtered for meat, so the majority of the population wouldnt know the difference enough to warrant the extra effort. I see it as kind of like them developing massive advanced tech to make all their meat turn purple; it's probably possible, but I just cant see how the motivation would develop.
PS In modern times not all cheese is actually Animal stomach enzyme (animal
Rennet), they have created a vegan version that is processed from a mold byproduct. Because mold poop is somehow healthier, I guess.