Don't forget that Skyrim's been a part of the Empire for a very long time. I look at it as the akin to state pride in the USA. Yeah most people like their state, but they are loyal to the country as a whole more so for the most part. It's not quite so stable in Skyrim of course, but I'm sure the Nords that consider themselves citizens of the Empire do not see the Stormcloaks as liberators. Hawaii is probably the most recent good example of this in my country. It was not at all friendly when Hawaii was subjugated by the USA many decades ago. Generations later I doubt most Hawaiians think of the USA as an oppressive occupying force.
I think it will be interesting to see the reactions to the other races. The Imperial forces did not seem malicious to me. Certainly cold, reckless, and unscrupulous but not outright malicious. Perhaps my opinion will change when the reaction to other races is revealed, but I would be surprised if it's much worse.
Someone commented in this topic about perhaps a disdain for refugees in the introdution. That is more likely from the native Nords than the Empire, I would suspect. The Empire specifically protected the refugees of Orsimir as they fled to Skyrim, and the government of Skyrim all those years ago took them in with open arms. The Dunmer were not exactly shunned either after the disaster in Morrowind. Those racial tensions have taken over a century to get to the point where they are in Skyrim. The Empire has no reason to not like the refugees. It's racial tension in Skyrim itself that's more likely to fuel that, and I'd expect that attitude to be more common in the Stormcloaks than the loyalist faction. The introduction really makes it hard for me to see the Empire as anything better than a misguided foe though.
I'm really hoping they show the Imperial forces as more multiracial this time around. The recent books made that quite clear, but I didn't get that impression from Oblivion at all. Perhaps that made sense since Cyrodiil is the home province of the Imperials though.
Stormcloaks are basically rebels/freedom fighters to free Skyrim from Empire control. An imperial will not exactly have a vested interest in risking his life to achieve that kind of goal. So he is the most likely to get a pass from the lady captain. The other non-Nords might or might not depending on how female-dog-y she is.
Edit: I totally misread your post, so I'm changing the above to a generic reply to the topic. I thought of this too. Why would they execute a random Khajiit they happen to catch at the same place as the Stormcloaks? I think she's just eliminating them all just in case. It's cold and barbaric, but I think that's why. If you want to put it in terms of women, I get more of an ice queen vibe than what you said at the end there.