Or, more specifically, for RP value, would it make sense for me to join with this character?

My character is a fairly laid back Khajiit, who is very loyal to his friends. When I escaped Helgen, I followed Ralof, so my character would now consider him a friend. I've so far just been doing the Dragonborn storyline, but was wondering if joining the war would be good with this character? Is there any particular side of the war that is more moral or would make the most sense with this character? Or would neither make sense for him, and therefore would it be best to keep him out of the war?

You know, from the logical point of view, I don't see any non-Nord joining Stormcloaks as particularly plausible.
But alas, Bethesda is too lazy to implement some deeper interaction ("nice armor you have there" seems to be more important than "hey you are a khajit. GET OUT!") so any RP value goes out of the window.

Just for the [censored] and giggles I played a High Elf and joined the angsty little rebels. Guess what. They let me in, and now you have a scene about Ulfric giving his hate speeches about Elves... with me, the mighty Altmer standing right beside him.

Epic fail.

I would say: yes, absolutely.

But there are already many love/hate stormcloak threads on this forum. You can find all arguments (and more) on those threads.

Hmm, perhaps I'll give it a miss with my Khajiit guy then, and do the quest with another race So are they against everyone except other Nords?

I think that, being a fairly laid back Khajiit, you would be happier remaining neutral, wandering the land, doing your own thing. Or at least remaining neutral until you feel strongly for one cause or the other. Personally neither side appealed to me much. My own (dark-natured) Khajiit did things his own way (I love revolution, but the racism on the part of the Nords was just too off-putting!)

Actually like I said, you can join them as whoever you want but thanks to Beth's lazy priorities it won't make much sense for a foreigner to join a faction with a motto "Skyrim is for the Nords!".
(Unless you role-play some greedy mercenary, but even there Ulfric talks to you like his right left hand)

And no, I wouldn't say they are againts "other" races, but they definetly have a bit of that racist-kind of complex, if you catch my drift.

Thanks guys, I'm thinking now I'll do the Stormcloaks questline with a different character I planned to make; a Nord who I intend to do the Companions questline with. Once I've completed the Companions, perhaps then I'll join the Stormcloaks