The problem is that you only get half the story when it comes to the Khajiit Caravan's - They are actually smugglers.
There are twofold reasons for that -
1. You were at Helgen with him
2. You come with the highest recommendations from one of his Top Leiutenants, who's life you saved.
He could at least mention something, though. Like, "Even though you're a Khajiit, my Lieutenant speaks highly of you. I wouldn't normally be so accepting of help from your kind, but you've shown where your loyalties lie."
Little things like that, for all races, from some of the more prominent characters would be quite welcome. But I think the only character in the MQ, after Helgen, to identify my race was when
Spoiler Paarthurnax told me to not greet him as a Khajiit, but as a fellow Dovah (or something to that effect).
Despite the racially charged tension among the Nords, they didn't care about my race one bit (made worse by how the Khajiit are typically allied with the Thalmor, whom neither the Stormcloaks or Empire like, yet no one ever questions you or remarks on that).
I really think the MQ could've had more encounters with the different races, both "good" and "bad". As it is, the people you encounter for it are essentially all human*, with some high elves, one bosmer, one dark elf, and one (optional) orc... and one khajiit, who doesn't say anything and tries to kill you moments later. I know that this is Skyrim, and Nords are going to be predominant, but it's pretty ridiculous how lopsided it is, IMO.
* And yes, I use "human" because Nords, Imperials, and Bretons are practically indistinguishable.
They DO care that you're dragonborn, they let you in the city!
And become Thane, and get a Housecarl, and buy a house.. just like any other race.
Another thing that really bugs me is that quest Ysolde has you do.
Spoiler She wants you to get items so she can trade with the Khajiit caravans, and build up a working relationship with them to allow them into the city. I thought, "cool, I'm a Khajiit, I can help her, and hopefully smooth over relations between the city and the caravan, maybe letting them inside." So I go about finding the items for her, give them to her, she thanks me, and... nothing. Nothing changes with the Khajiit, and she doesn't even seem to acknowledge their existence afterward. Not even a "I couldn't get the steward to agree to let the Khajiit into the city. I'm going to have to keep working at it." from her, or a "We met again with Ysolde. She's still trying to let us enter the city." from the Khajiit. Of course, it'd be nice if they did eventually get allowed into the city, but any acknowledgement about what I was trying to do would be nice.