What is the ruling on performing ablution (wudu') while having hair cream applied, knowing that it does not prevent water from reaching the hair, but the water mixes with it like soap?

If the head is wiped with water that has not changed [in its essential properties], then the change in the water due to what was on the wiped limb does not matter, provided that it was pure. The Hanbalis hold the view that a change in the water due to what was on the limb does not prevent purification, because it is a change that occurred within the place of purification.