During the tenure of Pope Paschal II, he presented the idea of church divestment as a strategy for ending the Investiture Controversy. Obviously the clergy did not approve of this, since it entailed a significant loss of influence on their part. As a result the planned divestment of the church was not followed upon.
Paschal's proposal was never a serious one, it was just a trick to gain time to stall Henry V and to cut down internal enemies. And everything ended in those strange and contraddictorial agreements of Sutri in 1111.
The proposal wasn't feasible because it wasn't anymore possible to tell the church allodia from the regalia. How distinguish from the rights heldby a bishop as a public official and those held as a member of the clergy? Consider that especially in north Italy this "confusion" dated back to before the creation of the Holy roman empire if not the late roman empire itself.
Not to mention that many bishops could support themselves and their large retinues (not only other clergy, but also knights, servants etc...) only through the exrcise of regalia.
Finally the emperor's goal was not to separate the church from the state, an idea absolutely outlandish for the times, but "only" to nominate the bishops.
Anyway, if we suppose that Paschal II manages to defeat his enemies, that Henry V accept the plan and finds enough administrators to substitute the bishops, that said bishops are funded to make up with their losses and all the protests are quelled down, you would definitly have a turning point for the western history.
The divestment would probably send the catholic church toward a more spiritual and less political evolution. Movements like the Cistercians and Franciscans could become far more successful than OTL, while the Lay powers would have free hand.
On the other hand the church could focus more on the pauperes rather the potentes and champion their cause against the nobles. The church, rather than acting to preserve social peace, like OTL, could become dominated by more radical istances and support a struggle to even the social disparities...
Of course if Paschal decision is not upturned by one of the following popes, something I would consider quite probable.