Answered by Ustadha Shazia Ahmad
Does washing the following body parts only once, fulfill the minimum requirement of wudu according to the Shafi’i madhab — washing face once, hands and arms once, wiping a single hair once, and washing each foot (and between toes) once?
Yes, washing those body parts, only once, does fulfill the minimum requirement of wudu according to the Shafi”i madhhab. However, there are two other integrals for a valid wudu in our school. The first is the intention and the other is that these body parts be washed in the order that you mentioned.
I have provided a link about the integral of intention, for further clarification:
Continuity of Intention During Wudu
And Allah knows best.