The person calls him or herself "Rav Aaron Samuel Tamares" (d. 1931) named after an Orthodox rabbi who embraced pacifism after becoming disillusioned with Zionism.
As of this writing, the account has only 28 followers - but they are almost all very prominent in Jewish anti-Zionist circles: Mondoweiss, Peter Beinart, Eli Valley, Jewish Voice for Peace, and many more.
This is clearly something that was set up to provide a supposedly Orthodox Jewish anti-Zionist voice, to shield anti-Zionists from accusations of antisemitism.
The account has tweeted only three times, and the tweets may be translations from some of the real rabbi's writings which were published in English only last year.
As of this writing, the account has only 28 followers - but they are almost all very prominent in Jewish anti-Zionist circles: Mondoweiss, Peter Beinart, Eli Valley, Jewish Voice for Peace, and many more.
This is a new twist on an old trick, as anti-Zionists love to quote religious anti-Zionists who lived in the early part of the twentieth century. However, after the state of Israel was born, the halachic framework on how to deal with Zionism changed - it was no longer a theoretical political movement but an actual home for a significant proportion of the Jewish people, ruled by Jewish people.
We don't know what Rabbi Tamares would have thought about Zionism after the Holocaust, or about the State of Israel after its founding. Outside of some extremist sects, most Orthodox Jewish thinkers accept and support Israel since the question of how to deal with it is much different today than the questions that Rabbi Tamares grappled with from 1900 to 1931.
For example, the pinned tweet "Political Zionism, as developed this far, clearly imperils the character of Judaism, which has survived so many centuries free from the defilements of nationalism" may have seemed true in the 1920s to some Orthodox rabbis. Yet today, Israel is the center of Jewish thought, and Orthodox Judaism is more dynamic in Israel than anywhere else. The leading halachic authorities today live in Israel and the most forward-thinking Jewish education is happening in Israel.
Tamares' prophecy was proven false.
This Twitter account is being set up to criticize a state that the real Rabbi Tamares may very well have supported.
Ironically, the entire purpose of this account and of those who support it is to politicize Tamares' words - when the rabbi himself was against the politicization of Judaism.
UPDATE: I made a major mistake - these are accounts that "Tamares" follows, not that follow him. (h/t Bob.) I regret the error.