Do all schools of thought (madhhabs) stipulate the use of water for istinja' (cleansing after defecation or urination) if the impurity exceeds its place, or do only some of them stipulate that?

The default is to remove impurities with water. As for cleansing with stones (Istijmar), it is a concession limited to the usual place from which impurities exit. The four madhhabs (schools of thought) have agreed that cleansing with stones is not sufficient if the impurity exceeds its usual place. The madhhabs differed in defining what exceeds the usual. The Hanbalis consider it to be the spreading of the discharge onto any part of the buttocks or its unusual extension to the glans. The Malikis consider it to be what exceeds the soft part of the anus and two-thirds of the scrotum. The Shafi'is consider it to be what exceeds the glans for the male and the buttocks for the anus. As for the Hanafis, what exceeds the exit point and is more than the size of a dirham must be washed by consensus, whereas what is on the exit point is considered as internal and is not combined with what is on the body.