I've been messing around a bit and it seems as though whenever FSB is rendering something, it renders the fog layer as the entire skybox. Interestingly, this means that if you go below the world, where the fog color turns black, the entire sky turns black too. I believe that this is a likely explanation for why all the skyboxes that use add blending look washed out.

Any news on when this will get fixed? The difference between OptiFine and FabricSkyBoxes is quite jarring.
Optifine:

FabricSkyBoxes:

This is because- it turns out- FSB does not render the vanilla sky during sunset and sunrise (or at all, during the day either?) but instead renders its own sky. So the texture blending looks different. A vanilla sky type was already added, but it's not yet published.

It's fixed in the development branch just be patient, it will be released sometime between now and the heat death of the universe. :)

With the release of 0.7.0, FSB has added overworld and end sky types.

For End Users

If you are a FabricSkyBoxes-Interop user update to 1.3.1 and conversions shall handle them automatically. If you are using MCPPPP, at the time of writing you will need to wait for the author to update and support it.

For Resource Pack Creators

If you are a resource pack creator please add them.

Here is an example overworld sky that renders the sunrise/sunset effect.

{
  "schemaVersion": 2,
  "type": "overworld",
  "properties": {
    "priority": -2147483648,
    "fade": {
      "alwaysOn": true
    }
  },
  "conditions": {
    "worlds": [
      "minecraft:overworld"
    ]
  }
}

Here is a decorations overlay if needed.

{
  "schemaVersion": 2,
  "type": "monocolor",
  "blend": {
    "type": "replace"
  },
  "properties": {
    "priority": 2147483647,
    "fade": {
      "alwaysOn": true
    }
  },
  "decorations": {
    "showSun": true,
    "showMoon": true,
    "showStars": true
  },
  "conditions": {
    "worlds": [
      "minecraft:overworld"
    ]
  }
}