Okay, so they don't welcome outsides...but yet seeing them run around the city isn't the least bit shocking?
Do remember this outsider is sponsored by one of their high noble houses, and has the famous reputation of slaying the gigantic dragon that was rampaging through the Steps of Faith. Most Ishgardians are savvy enough to know one does not mess with someone who is that powerful and has a powerful noble's backing, and the ones that do get plenty of exposure in the story.