There are staunch anti-zionist factions such as (some of) Brisk and Satmar, Toldos Aaron, etc. that are diametrically opposed to the Zionist regime (referring to it as heretical and such). According to these groups (or similar groups) is making Aliyah (i.e becoming a citizen of the Zionist state) halachically forbidden?
No. The Satmar Rav was in fact going to move to Israel after he escaped Europe, but saw the number of Gedolim there and felt he would be of more use elsewhere. The Griz moved to Israel and founded a Yeshiva of Brisk. Their opinions led them to hold that it is permitted to live in Israel, even a mitzvah, but is forbidden to have anything to do with the govt.
In short: Those living in Israel will avoid making aliya, but might be Israeli citizens none the less.
Without delving into specific groups or the political aspects, it is worth noting that most anti-Zionists do not oppose living in Israel but rather question the legitimacy of the state of Israel. They may choose not to actively pursue Israeli citizenship. It is important to mention that individuals born and raised in Israel automatically possess Israeli passports upon entry, but some anti-Zionists prefer to avoid obtaining these documents as it may be seen as a sign of support for the state.
When discussing Zionism and living in Israel, three main issues are often raised.
The first is the argument that the Gemora describes three oaths https://en.wikipedia.org/wiki/Three_Oaths taken by the Jews, one of which is not to ascend to the land en masse ("שלא יעלו ישראל בחומה") and העולם שלא ימרדו באומות they shall not rebel against the rule of the nations of the world According to this viewpoint, the Gemora forbids going against the British Mandate in Israel and to arrange mass emigration.
The second argument pertains to the loss of Jewish lives during the establishment of Israel and subsequent wars. Those who question Zionism ask who gave us the right to claim a country as our own if it results in bloodshed. Wars are typically justified in cases of Pikuach Nefesh or when mandated by Hashem through the Kohen Gadol or a Navei. However, there was no need for Jews to be killed for such a cause, as argued by this perspective.
The third argument is based on "Daas Torah" (the opinion of Torah scholars). Although a few rabbis supported the establishment of the State of Israel, the majority were against it. Going against Daas Torah, the collective wisdom of Torah scholars, is seen as unacceptable in this context.
These reasons form the primary basis for the assertion that Israel has no right to exist, while acknowledging the religious obligation to live there. However, this viewpoint does not grant legitimacy to the government. It is important to note that these arguments have been extensively discussed and debated, and this response merely aims to answer the question without expressing personal opinions. The information provided is derived from a yet-to-be-published book by an author who holds an anti-Zionist stance and requested constructive criticism, which was provided. This response does not reflect my personal opinion in any way.