Current DSD recordings are real time recordings without the possibility of post processing for instance. So not much in the way of manipulation.
Sony sells a mastering platform for DSD, and some DSD content was captured with hi-res PCM and then converted to DSD for release.
I certainly consider equalization to be post-processing.
I master digital recordings that I record live (any mixing is in the analog domain of the real time performance) as a hobby. I limit the mastering to:
-filtering out DC offset
-applying a noise reduction filter
-fading out the noise floor at the end of the recording so it does not audibly fall off a cliff at the end
-trimming the lead in
-setting the digital level and checking with an anti-clipping filter (which checks for digital clipping, does not modify the file)
-dithering down to the release format with noise shaping
-rechecking with an anti-clipping filter as a precaution
I don't use equalization-- the listener can use equalization to adjust for their speaker, ears, and room if they want. I also do not do compression. You would certainly want the steps I listed other than dithering down to lower format done for a DSD recording, the noise reduction step especially if a MIC was used.
A professionally mastered recording will have whatever post-processing makes it sound best for the targeted uses. That's the mastering engineer's job. With high-res content, the mastering engineer assumes a high-fidelity playback system, and is freed of the burden of having to try to make it sound as best as possible on everything from boom boxes and car stereos to audiophile systems. That is actually the biggest benefit of high-res formats over Redbook.