^Well, yes, of course any government has opposition, but my point is that Martok's position is now much more solidified; he has broader, stronger support and is in a much less tenuous position of leadership than he was before. So there's substantially less risk of some militant faction overthrowing him than there was before Destiny. Waiting until there's zero opposition is absurd because it will never happen, nor should it. A state with no opposition is an absolute dictatorship. What you want is stability, and that's what Martok's government has now, more than it did before.
Emphasis on the now. With several planets in ruins, with hundreds of starships destroyed, and considering the fact that the Empire was, culturally, never really very big on or receptive to the "softer" fields of study (agriculture, science, etc.), life is going to be harder than its ever been before for the Klingons. And when the grumbling starts, there's always going to be someone who will take advantage of the discontent.
Also, we have no idea how the makeup of the High Council will end up. In politics, more often than not, a majority is transitory, particularly when it comes to the aftermath of an emergency situation.
Also, the way the UFP and the Klingons fought together against the Borg has resolidified their ties. The Klingon people now see Martok as their victorious champion and the Federation as their stalwart partners in the struggle. Any lingering anti-Federation faction would have a hell of a hard time winning support for a coup. It's foolish to go up against a war hero, especially in a society that esteems warriors so highly.
That may be how it seems now, but sentiments of groups who try to tap into what will seem like a populist stance, like those who oppose the Federation are not, nor ever have been, bound by reality or logic. Further, the Klingon Empire has had its share of leaders and groups that, it would appear, would be working at a counterintuitive purpose. Look at the group Klahb. Look at General Chang and the others who tried to derail the First Khitomer Accords. Look at Gowron. Look at Kravokh.
and the fact that the Tholians and other groups who didn't join with the Federation were also left alone
That's not true. The Borg expanded outward from their entry point and slaughtered indiscriminately, regardless of allegiance. Nonaligned worlds fell too -- including the first two casualties, Acamar and Barolia.
I wasn't counting Acamar and Barolia. The Tholians, the Breen, the Tzenkethi...they didn't join the fight and they didn't get attacked.
Now, logically, that doesn't mean they wouldn't have. But it's a convenient argument to make, especially when you want to blame someone else. Further, the Federation are seen as having provoked the Borg, and so why should another group get involved when "they were asking for it"?
Logic and reason have absolutely nothing to do with most political ideologies, particularly those who try to adopt a populist stance.