The Targs didn't conquer the Iron Throne: they made it. They're also the reason that there's a unified Seven Kingdoms or why Kings Landing or the Kinsgaurd exist. There's a reason that one of the name's of the Rebellion is The War of the Usurper. It's also the reason that Robert was the one to take the throne. I'm not sure if it's ever mentioned in the show, but Robert's Targaryen bloodline (his grandmother was daughter to a Targ king) made his claim to the throne stronger than any of the others involved in the rebellion. That's why he goes through the trouble of hunting down the remaining Targs. Besides them coming back for revenge, they can easily use claim arguments to rally support.
But at the end of the day might makes right, so if people really do end up squading up with a particular side it'll be because they like the chances of winning better on that side.