Hi Emanuele,
There's nothing wrong with your color management setup in PixInsight. Just something that you should probably change: the rendering intent for your screen profile should be perceptual instead of relative colorimetric (it doesn't make too much sense trying to match the white point of a monitor profile). However, this is not a practical problem at all.
Come on with the things that you may be doing wrong:
- If your image is a grayscale image in PixInsight, then don't embed a sRGB profile when you export it to other applications. PixInsight supports both grayscale and RGB color profiles embedded in grayscale images, but this is a nonstandard PixInsight feature, not supported by other applications.
- Never embed an ICC profile in any image for web deployment. Even web browsers supporting color management don't produce valid color renditions of images with embedded ICC profiles (e.g., Firefox). Always leave your web images untagged (no ICC profile embedded) and be sure their pixels are meaningful in the sRGB color space. To achieve this goal, follow these rules:
* If your default RGB (or grayscale) profile is sRGB (as it is in your case), then do nothing. Just save your images as they are and (as they are intended for web deloyment) be sure
not to embed an ICC profile.
* If your default RGB (or grayscale) profile is not sRGB, then before saving your images for web deployment, use the ICCProfileTransformation tool (ColorManagement category) to convert them to the sRGB space. Again, be sure you don't embed the sRGB profile (nor any other) when you save your images.
- To maximize the chances of your images being seen correctly on the WWW, try to avoid too dark backgrounds. Many people tend to have too low brightness settings, and most cheap monitors are poor at reproducing detail in the shadows. As a general rule, for a deep sky image the main histogram peak should be around 0.1 or 0.12, roughly.
- As a general recommendation, avoid embedding ICC Version 4 profiles in your images, as not all applications support them yet. For compatibility, better embed ICC V2 profiles. This is not a big issue though, as PixInsight fully supports ICC V4 and, why use other applications?

- Always bear in mind that implementing color management on the WWW is an extremely difficult task, if not a completely impossible task. Following the above recommendations is about everything you can do to ensure your images will be seen as they are intended to be seen, but even then, a lot of people won't see your images as you expect, and a fraction of them will see your images horribly. We have to live with this, at least for now.
Hope this helps.