No more so than Nords. They aren't allowed in any city no matter who is in charge.
Khajiit
caravans are not allowed into cities because of their contribution to the skooma trade. J'Zargo was able to enter Stormcloak-controlled Winterhold and join the college at some point, so apparently law-abiding Khajiit are allowed in cities.
That and, what are the Khajiit redeeming themselves for anyway? they didn't do crap directly to the Nords, the (majority of) Nords are just completely racist.
The (majority of) Nords don't even say racist stuff in the game, so where do you get this generalization from? Anyway, the Khajiit have built a reputation up throughout Tamriel as thieves and drug-dealers. Unfair, yes, (as unfair as saying Nords are mostly racists) but that would probably be what OP is referring to.