Is it obligatory to perform Istinja (washing the private parts) for the next prayer's Wudu (ablution) after passing wind?

There is no obligation to perform istinja' (ritual cleansing after defecation or urination) for the emission of flatulence, nor is it prescribed in the first place. Whoever does so believing in its prescription has committed an innovation (bid'ah). Istinja' is performed after the discharge of urine, feces, madhiy (pre-seminal fluid), wadiy (thick white fluid that may be discharged after urination), and similar substances that exit from the two private parts and leave a trace. Imam Ahmad said: "There is no istinja' for flatulence in the Book of Allah, nor in the Sunnah of His Messenger."