Picture Styles do not change the underlying RAW sensor data. When you shoot RAW, the selected style is stored as metadata and used for the embedded JPEG preview, the image shown on the camera LCD, and often the histogram, which is usually based on that preview rather than the RAW data itself.

If you open the RAW in Canon Digital Photo Professional, it will usually start by rendering the image with the Picture Style that was selected in-camera, but you can change it later without harming the RAW file.

So, when shooting RAW, choosing a Picture Style is mostly about preview and workflow convenience. If you already know the look you prefer, setting it in-camera can save a step in post. Otherwise, it is not destructive.

As for Neutral vs Faithful: both are intended to be less punchy than Standard. From the provided answers, Faithful uses a 5200K white balance reference, while Neutral uses a more automatic approach. Another explanation given is that Neutral uses perceptual rendering and Faithful uses colorimetric rendering, affecting how colors are mapped into the output color space.