We know that the White Cloaks have drastically changed from their roots as non-violent preachers. We know their views have changed over the centuries by their own admission and the information provided in the BWB.

If they get used to fighting alongside channelers, then their animosity could fade. And if Galad, their trusted Lord Captain Commanders and someone who shares their religious views, turns out to be a channeler. Then it is possible that they could come to accept channeling and channelers as not being dark friends.

What is strange is that they call Aes Sedai Dark Friends - but at the same time they are quite willing to accept that they will have to fight side-by-side with Aes Sedai at against the Dark Lord during the Final Battle. This implies that they are able to get over their animosity towards Aes Sedai, and that they really don't hold channelers to be Dark Friends at all.

I suspect that the Children (originally at least) see the White Tower not as being forsaken by the light, but (given the Aes Sedai's association with the breaking) instead as corrupt rivals. Like any religious fanatics.