I recently read Anne Watson's book on milk soap making and if I'm remembering correctly, yogurt is one of the only milk products she found works better if it is used at 50%. She did many, many experiments with various milk products, including vegan versions. Using the split method recommended above would make it easier (lye dissolved in a portion of the water, yogurt added to oils as the remaining liquid). Maybe this is because yogurt is high in solids compared with milks.
ETA: I checked the book, and there’s not much detail except that she recommends mixing both yogurt and sour cream with water 50/50 to avoid getting marbled streaks through the soap. All of her recipes for liquid milks (any milk product that is not in powder form) use frozen milk to dissolve the lye. She uses the split method, but only for adding powdered milk to warmed oils.