The question for someone over on the Agudah end of the spectrum (as well as some others) can be boiled down to this: With the arrival of Mashiach, we can safely assume that the nation then established will require police, a fire department, courts, sanitation, an army- maybe even a parliament. As the modern State of Israel supplies all such things, isn't it logical to assume that they will simply continue (as, lehavdil, Mandatory institutions did)? And if this is the case, isn't there some level of significance to the State as a first step toward an age of Mashiach? (I won't approach of the question of whether the modern day State, with some ideological changes not outside the realm of possibility, might one day accomplish the acts required of Mashiach without there being one recognizable [at least at the time] individual in that role.)
To someone of the Satmar or Neturei Karta persuasion, the answer is not difficult: No. To them, the State is an evil that must be entirely swept away, consequences be damned (although they're blindly not really concerned about those), before a Messianic age may arrive. But they're evil gits. I'd like to assume that the Agudists are not.
But I don't have much cause for optimism. In another context, Meir Kahane would say, "I say what you think," and sometimes I wonder if Satmar fulfills that role for much of the Charedi world.
For example: You can't get much more mainstream charedi than Artscroll. Once, out of curiosity, I looked into the Artscroll Talmud to see what they say on the "Three Oaths." Now, they could simply say, "There's too much to discuss here, and there are numerous opinions." After all, it's not halakhah, and it doesn't play much of a central role in Judaism to anyone outside the Satmar. And, indeed, Artscroll begins its comment with exactly that line. However, a few pages later, it goes on- despite its own introduction- to give one point of view. It doesn't say there are other views, and it never mentions that the view it gives is the most extreme, namely, that of the Satmar Rebbe. It's too identical to be a coincidence. I imagine that almost all of the Modern Orthodox Jews who are Artscroll's main market, and almost all of the Charedim who use this Shas as well, have no idea what it is they're being presented. This is troubling- far more than the relatively silly ways in which Artscroll sanitizes history or translations or Bible commentary. And yet no one, so far as I know, has commented on it. (Off to Google...)