This is not definitive, but I'm pretty sure it alters the odds of a planet flipping on any given turn. Once you get a planet above 4, each turn the game rolls a random chance of that planet flipping. To pull numbers out of my ass, say 10%. The Yor loyalty bonus would reduce this to a 5% chance, thus making their planets more resistant to flipping without making them completely invulnerable.
If I'm not mistaken, this was how the unfortunate MCC bug worked. Instead of raising the chance of a planet flipping to 100%, it dropped that chance to >1%. Planet flipping was possible, but totally impractical. Also note the fixed MCC completely negates any loyalty bonus.