Ultimately Shrek is, at his core, a Selesnya personality.
His underlying authentic self is kind, thoughtful, loyal, and good (white)
His underlying self is content with the simple life, desires harmony, and is at peace with the natural world (green)
Placed on top of that, due to a lifetime of prejudice and rejection, are environmentally-developed Rakdos traits
He was forced into a hyper-individualist self outlook (black)
He falls victim to emotional outrage and lashes out with quick temper, anger, or wise-cracking defensiveness (red)
We can also mention that he has cultural and species ogre values that are very different from many of the other creatures in his world. He and Fiona have hobbies, mannerisms, and hygiene that other find disgusting but are clearly actually in harmony (green) with his own natural needs). And, you could even argue that Shrek has a very philosophical side as well. He has clearly thought deeply about how the world works and why. Which would even push him into Bant if you wanted to especially emphasis this aspect of himself.
Anyone pushing his surficial traits of being an ogre (sterotypical red tribe) and living in a swamp (black environment) are falling prey to exactly what the movie wants us to avoid doing - not stereotyping. Seeing the real person under the surficial traits. Understanding that what's a genuinely lovely and enjoyable home for Shrek (the swamp) is a wretched and vile environment for humans. Because different people have different needs.
