I was reading khajiit lore,and apparently there was a time known as the "void nights" when for 2 years the moons did not shine.It was really more of an inconvenience,except to the khajiit. They COMPLETELY flipped out,because there entire culture was based on the moon,moon gods,etc.When the moon came back,the thalmor took credit and the khajiit believed them.Any idea how accurate this is,and if the khajiit really do support the thalmor?

Well, they are a province of the Dominion. And they have (from what we've seen in Skyrim) cooks and assassins in Thalmor ranks.

According to the book, "http://www.uesp.net/wiki/Skyrim:The_Great_War" this is true, yes.

It's not clear how many of the Khajiit buy into the Thalmor propaganda about the moons.

Some Yes but like all things, probably not ALL of them do.

Also, "support" may not be the right word. Politically, the two Khajiit kingdoms are subordinate to the Aldmeri Dominion. To what extent the rulers of those two kingdoms share the Dominion's ideals and goals of the conquest of Tamriel, is not clear. (Although, it is suggested that the rulers of the two Khajiit kingdoms may be Thalmor puppets).

Pellitine and Annequina (the two major regions of Elsweyr, now reformed as governments) are currently client states to the Thalmor, so apparently it was enough for the Khajiit rebels and Thalmor coup members to take control, but things can get hectic with Thalmor politics.

It's written that when the Thalmor allegedly saved the moons, the Empire lost so much influence in the area that it became vulnerable to rebellion.

I think the common Khajiits merely don't like the Empire, are ambivalent to the Thalmor, and want some moon sugar immediately. Maybe we'll get more information later.