If, as a Cathar, I Holy War an excommunicated Catholic, will other catholics help him?

Solution 1:

Yes. An excommunicated Catholic is still a Catholic and nearby Catholics can still join his war- it doesn't matter if they're under attack by a heretic or a non-Christian.

They are, however, a lot less likely to. Joining a war is based on opinion- since excommunicated characters get -30 opinion with all Catholics, his neighbours probably hate him at least as much as they hate you for being a heretic.

You might also be able to attack while some of his neighbours are already attacking him for being excommunicated- in that case they can't join him.