How does Satmar, Neturei Karta, and other similar groups view Religious Zionists and Haredim that interact with the Israeli government, from a halachic standpoint (i.e. are they acceptable as witnesses, etc.)?
Rav Yoel Teitelbaum held that interaction with the government itself may be a yehareig v'al ya'avor, but the Neturei Karta (N"K) seems to hold that for ALL people in Israel. R'Yoel also wrote that it was assur to visit the mekomos kedusha because it brings hana'ah to the government.
I'm primarily going to address the opinion of Satmar:
But failing to allow oneself to be killed for a YvA"Y isn't itself a severe sin punishable by death (when it's not one of the big three). So halachically, you aren't optimally keeping the Torah, but it's not on the level of, say, being mechallel shabbos.
This implies that they are still treated as Jews for all other relevant halachos by those groups. Any objections to someone on these grounds is purely "moral" and wouldn't seem to be upheld by even their own halachic teachings.
For N"K, there are those who may believe that an oleh, by violating the shalosh shevuos, may be considered a Rodef (because by his actions they endanger other Jews). If this is the case, then the question arises as to whether this person is consider a "nidun binafsho" halachic non-entity: "since they're chayav misa, they are not considered to be alive" - though it's questionable whether you can apply this standard to someone outside of a ruling from Beis Din.
An additional consideration for N"K is whether they consider such a person inherently a rasha (and therefore invalid), a tinok shenishbah, or simply a misguided person acting out of teivah. The latter two categories wouldn't be invalid for other purposes (ne'emanus, eidus, etc.), while the first would.