If they had to pick a side, many Redguards would most likely side with the Stormcloaks given that Hammerfell has no love for the Empire after the WGC and resulting secession. The Stormcloaks really just want what the Redguards in Hammerfell wanted and were able to achieve- their land free from the Empire's control. Anyone with ties to Hammerfell could easily sympathize with the Stormcloak cause.
I think a Hammerfell/Independent-Skyrim alliance would work out great, given the warrior cultures of the two lands and mutual dislike of the Empire/Thalmor. Redguard battle prowess and Nord resilience/brute strength would make for good chemistry.
Because he supports the Aldmeri Dominion and wants to stir up trouble. That was my reasoning for trying their quest line in a non-research way when I did a RP.
Why would anyone join the Stormcloaks? That is pretty easy. Because the character wants to oppose the Aldmeri Dominion. Because the character believes in freedom from the tyranny of a foreign power. Because the character believes in religious freedom. Because the Empire tried to murder them at the start of the game.