How acidic does a mixture have to be for milk to curdle?
Milk's natural pH is about 6.5, just slightly acidic. If it approaches a pH of 5.5, the casein proteins lose their negative charge and the micelles no longer repel each other, meaning they start to gather in small clusters. At around pH 4.6, the scattered proteins bond to each other again and begin to curdle. 

Though this kind of curdling is not the same as when making cheese with rennet.

I don't know what proportions of milk and vinegar you need to keep the milk from curdling but using pH levels you should get a pretty good idea.