From what I remember of Enterprise, I always thought the Andorians came off as reactionary and aggressive, but perceived themselves to be the aggrieved/oppressed party, who were under threat from the Vulcan High Command.
This might be my blindness to liking Jeffrey Combs too much, but I never got a view of Andorian supremacy from Shran. I think he initially demeans Archer as a "pinkskin" because he thinks humans are just a puppet-client species of the Vulcans who will be their lapdogs.
I mean if we go down this road, what are McCoy's "green blooded, pointy-eared..." insults towards Spock?
I don't think McCoy is a bigot any more than Shran. Both Shran's "pinkskin" nickname for Archer and McCoy's ribbing of Spock is supposed to be seen as signs of good-natured respect between people who are close enough they can use cultural insults and it's not supposed to be offensive.
But if you apply modern standards about race and culture to species in Star Trek it can be viewed as problematic, since it fits the behavior and a line of defense used by people who say and do things that upset others and go "come on, they don't mean anything by it."
Swap McCoys insults in the 1960's for a IRL setup if Spock was a nonwhite human, e.g Sulu or M'Benga. In universe it is still unprofessional behaviour. As for Shran, used the term 'pinkskin' before he and Archer built up any respect, it was meant to be an insult. But because most of us like the characters we give them a pass, that they would not get in a real work atmosphere.