The rank and file charedim don't. It's their traitorous political parties that sit in governments of seculars who do give away land, and who do themselves support it (ie Rav Ovadia). But the rank and file haredim often go along with the rabbis, but talk to some of them and see if they think it's a good thing. Most don't, unless you are talking to Naturei Karta or a Satmar (only some Satmar). In fact, many cite it as yet another reason why the evil zionist state is so evil - they threw all those Jews out. They probably think their "leaders" and rabbis are powerless to oppose it so they don't blame their traitorous parties for going along.
You are largely correct. There is a big difference between "rank and file" Haredim and hardcore NK/Satmar enemies of their own people. The average Haredim just go along with whatever their rebbes and political leaders say, but are not necessarily hardcore about it by any means. With a potent right-wing voice in Israel, I am sure that no small number of them, particularly in the younger generations, would ditch Shas/Agudah and join Hayamin.