The thing with the Dither_8BitColor node is that it is creating noise because the colors on your model don't match any of the 64 colors in it's palette. the reason it is creating noise is because it is trying to mix the colors visually.
I looked at the twitter post you sent me and I think the best way to get that look is by using the Dither-Bayers_ThreeTone node with a color ramp or my color ramp math node like this.
I would put the BSDF through the color ramp to make the shading more crisp and have the texture added after using the Dither-Bayers_ThreeTone node.
The settings I used in the above image I think best match the style of the twitter post you sent me but the look could be different by changing the values in the color ramp and Dither-Bayers_ThreeTone nodes.