In what ways was the church involved in the feudal system

Catholic bishops were involved in crowning kings and emperors (who were at the top of the feudal system). In Germany, 3 out of 7 sovereigns who had the right to elect a new emperor were archbishops.

The catholic church also rented land as fiefdoms to to lower peasants, just like the aristocrats did.

Due to some historians, the chuch was the biggest liege in the high middle ages (25 - 50% of all fiefdoms being owned by the church).

Furthermore, the church gave a legitimation to the feudal system

by declaring that every man should work in the place where he was put (by god) and that the peasants should work, the clergy pray and the sovereigns protect. Since the feudal system is based on the idea of a sovereign protecting weaker ones and receiving tributes in return, this idea matched the idea of feudalism.