How should I connect PVC plumbing for two sinks to old cast iron stack with two threaded tees?
I'm keen to remove cast iron wherever it's practical to do so. In my experience, cast iron older than about 40 years can really get crudded up and slow. That said, removing sections of a stack can be challenging--you have to fit between nearly immobile sections and you have to support the stack while you work, or you have to replace everything going upward all at once. 

I'd see if you can get a nipple threaded into the upper hub just as we see in the lower one, using thread paste, and leave the lower one in place. Connect your new PVC to both nipples with shielded no-hub couplings. Be sure to bore out any corrosion in the cast iron hubs to the inner diameter of the nipples.

If those hubs are 1-1/2" or larger, that may be enough for two sinks. You could just plug the upper one and connect to the lower nipple.