The Ben Ish Chay (year 2, B'shalach 20):
Sometimes people make the aforementioned yogurt before Shabas: they heat milk, put it in a receptacle, and put a little made yogurt (or other binding thing) so this milk will harden and become yogurt. It's done by morning.Chaye Adam (Shabas) 16:11
But sometimes they see in the morning that it's still milk: it hasn't hardened to become yogurt. So they cover it with cloths and put it in a warm spot to finish it up so it hardens; some also put a piece of bread in it, also to finish it up. It's forbidden to do this on Shabas; rather, it should remain the way it is until it hardens and is done by itself. See Chaye Adam 16:11.
…Someone who adds vinegar or bread (or the like) to milk [on Shabas] to make it into yogurt (لبن in Arabic) — this is forbidden; see Chaye Adam.
It's forbidden to put vinegar or other things in milk [on Shabas] so it becomes whey, as that is actual choosing.
(As far as I know, milk doesn't become only whey when you add vinegar; I assume the CA
means that the milk becomes some product that includes whey. A tip of my hat to Stephen G. Brown
for the translation as "whey".)
(Note that Mishna B'rura 319 and Aruch Hashulchan 319 don't seem to discuss yogurt. As always, for practical halacha, consult your own rabbi.)