What are these white fatty granules that may be found after cleansing with water (istinja') from the anus, are they pure, and do they invalidate ablution?

We have no knowledge of the true nature of these granules; doctors should be consulted about them. As for their ruling, the basic principle is that whatever emerges from the two private parts is impure (najis), as mentioned by Ibn Uthaymeen. Accordingly, these granules are impure. Their emission nullifies ablution (wudu') according to the majority of scholars (Hanafi, Shafi'i, and Hanbali schools), whether the emission is habitual or unhabitual, small or large in quantity, and whether it is pure or impure.