If Irgun and the Stern gang didn't have popular support it would have been trivial for the Haganah to disarm them at any point in the 1940's. Instead, the Haganah frequently cooperated with the irredentist groups. The "good cop, bad cop" analogy is exactly right. The groups were useful for handling sensitive tasks that jeopardized international Jewry's support for the Yishuv. Irgun coordinated the attack on Deir Yassin with Haganah liasons. After the fact, the Yishuv leadership denied that and wrung their hands. How could they have know that they would commit a massacre against civilians? What an unforeseen tragedy...
Haganah only cooperated with the Irgun for a short while during the Jewish Resistance Movement which fell apart shortly when the Irgun went too extreme for their tastes.
To understand more You might want to read about the Saison where the Haganah cooperated with the British authorities against the Lehi and Etzel which had hundreds of members arrested.
Regarding popular support, due to management of immigration by the Jewish Agency and the facts of life in Israel at the time, the population was overly Socialist as I mentioned before, which can be seen in the respective parties sizes, this meant the politically they were completely on the other side of the political map.
It was also common for mainstream opinion to describe the Etzel and Lehi as terrorists, as can be seen for example in the 1946 World Zionist Congress
That is patently false. Publicly, the Yishuv was against underground organizations. Privately, there was much cooperation and coordination.
For example, Haganah handed Deir Yassin as a target to Irgun because they knew their fighters were ill-equipped to take on well-defended objectives. Indeed, they almost failed to capture the village so the Palmach had to come and help them quell the Arab resistance. The humiliated fighters took a bloody revenge on the Arab villagers. Afterwards, the Yishuv feigned outrage over the terrorist groups barbarism.
Later that year, Lehi murdered Folke Bernadotte. The Yishuv, again, feigned outrage and had many members arrested:
"Subsequently, many Stern members were disarmed and arrested, but nobody was charged with the killings, and the case, which was barely investigated, was closed. Stern suspects were detained after the assassination, but they were not treated like other prisoners. As Time magazine reported, these prisoners at Jaffa made their own rules, ripped bars from the windows and tore down the steel doors connecting their cells: “The Sternists threw open the door of the jail, disarmed the guards, directed traffic in the square where a great crowd had gathered. Some prisoners strolled off to the beach for a swim. Others relaxed with prison guards over coffee in a nearby café.”"
