Didn't someone say that the Minds exist in a hyperspace as defined by their novels? Such a realm would have no connection to the Warp, and so the Minds would be immune from all corruption unless they physically go to the normal universe.

The only reason you can assume the Warp can corrupt a Mind is because you make the basic (but necessary for this discussion) assumption that the Culture and W40K occupy the same space: the physical universe.

If the Minds exist in a Culture Hyperspace dimension, that is equivalent to a hypothetical situation where the Oldcrons successfully separated the Warp from normal space. The Warp Gods would be unable to interfere in the normal galaxy. Similarly, the Warp is unable to effect anything in Culture Hyperspace.

Addendum: The Newcron fluff sounds like absolute ***t. So what happened to the Nightbringer, Deceiver, Outsider, and Void Dragon? Erased?