Isn’t there harm to the living organisms in yogurt?
Yes. In Jain dharma, yogurt/curd is generally considered to involve harm to living organisms, because it is a fermented dairy product and contains micro-organisms. From the Jain point of view, any food that involves injury to even subtle life is to be avoided as far as possible.
In strict Jain practice, especially for sādhus and sādhvīs, curd/yogurt is usually avoided. Among householders too, many observe restraint with such foods, especially when following a more rigorous vrata or during specific periods of discipline.
So the short answer is: yes, Jain ethics recognize harm in yogurt, and it is often avoided accordingly.