There's no real hard line definition between a warp god that is chaos and one that is not. They are all chunks of sentient warp energy.

There have been a lot of attempts to visualise what this means - some venn diagrams that show overlapping chaos gods and how all the other gods are but sections of them (mork might be where khorne and tzeentch overlap for instance).

It depends how distinct a warp god is from the warp itself, whether they are literally part of the fabric, or distinct chunks floating around. If they are part of it, then they are all joined to each other in a metaphysical way. There is no true independence. Only in realspace can khorne fight nurgle, otherwise they're all a giant smoosh of energy.