I think it was a couple of factors. One, they wanted control, that was the driving force of their faction, and the "bad side" to earthbending. Stagnation, totalitarianism, rigid obedience to the laws that are unchanging and uncaring. The saw in Azula, that she was capable of control on a crazy level, so she would be of use to them. Also, she had clearly shown she could infiltrate their society and break it down from the top down with little to no effort. So trying to stand against her, and by extent, the Fire Nation, when it seemed clear they were about to be an occupied state, just didn't seem prudent to them. They were opportunists, looking out for their own self-interest. Azula was more than happy to let them keep playing their games of control, as long as they understood SHE was the one in control. That was fine with them, as it ultimately meant the same end result, them with a strangle hold on the city, just under a different flag.