Argonians also are allowed into the city, you as lizard can walk in for example, it's just that as far as living arrangements they're forced into the docks. Not to pull any punches here either but one of them is a drug addict who asks you to steal drugs for him.
What I don't get is why we're bringing this up like it's something actually worth talking about in the grand scheme of things as far as the Stormcloaks and their goals go. Every race in Tamriel is racist, except maybe the Imperials but after throwing the entire Nord race under the bus it's kind of in doubt for me, i.e the dark elves are so xenophobic that they hate other dark elves not native to Morrowind, and examples like these apply to every race. Why single the Nords out specifically for being racist? The Thalmor are so racist they want to kill every single race that isn't them or the wood elves, and they use the words "purity" and "race supremacy" while doing so.
I do agree that it's a shit time, but it's a rebellion motivated by anger at the Concordat and how Torygg sold out despite the disagreements from the individual Holds. Not much logic or planning is gonna apply besides "how hard can we fuck these Imperials up".