I don't think what you're asking is entirely possible. CSS cannot distinguish between images posted by one user and another user. A userscript probably could, but writing one for you is outside of the scope of my time and abilities at the moment. On top of that, even if you have user themes disabled, Neospring won't apply your CSS to another person's page.

However, after extensive searching on Mozilla's developer site, I did find a way to set everything except your banner and profile pic to sepia - basically, you need to set ALL images to sepia, then individually specify the ones you would like not to be sepia (using the end of their URL):

img {
  filter: sepia(100%);
}

img[src$="yourusername/banner"], img[src$="yourusername/avatar"] {
  filter: none;
}

If you just want avatars to be set to sepia (not other users' embedded images), this may work:

img[src$="avatar"] {
  filter: sepia(100%);
}

img[src$="yourusername/banner"], img[src$="yourusername/avatar"] {
  filter: none;
}

You can also exclude (or include) all emoji (no matter who posted them):

img[class="emoji"] {
  filter: none;
  /* or: filter: sepia(100%); */
}

And if you have a unique string that's present in all of your image URLs (unlikely unless you have a personal website), you can exclude/include that too:

img[src~="image-by-waluigi"] {
  filter: none;
}

This is somewhat annoying and likely to break when Neospring updates, but I honestly doubt that a better way exists.