I believe it is only the Khajiit caravans that are banned from cities because the Nords fear they are only pickpockets and skooma dealers, being Khajiit merchants. Adventurers are apparently okay in their eyes.
Yes, i never got an impression that khajiits are illegal in Skyrim

And there is a khajiit citizen in Riften.
Then again, can you really blame the nords? Almost all khajiits you encounter do try to kill you

Do you remember how to get the taste of Khajiit cooking out of your mouth?

I still have a hard time imagining them being so flexible
