For a time they were working with Irgun to try to establish "street cred" (my term). According to former officers with both Haganah and Irgun, Stern gang & Irgun got permission from the Haganah commander to lead the attack on the Arab village of Deir Yassin during the 1st civil war (Apr 9th, 1948). Whether he did this to spare his own troops, or whether he wanted Stern/Irgun to open a can of whup-ass on them, or whether he simply couldn't control them I couldn't say, but I suspect the latter.
When they found the village was full of Palestinian fighters, they went house-to-house, throwing a grenade in the front door before entering. That the Palestinians were using civilians as human shields cut no muster with them and they killed women and children along with the Arab belligerents.
https://en.wikipedia.org/wiki/Deir_Yassin_massacre
Which sounds brutal but they were still in the same decade when a third of their people world-wide had been exterminated for being Jewish, and they obviously were fed up and in no mood to let anything prevent them securing a homeland where they could control their own security and fate.
From the article you cite:
“Yoma Ben-Sasson, Haganah commander in Givat Shaul, said after the village had been captured that, “there was not even one incident between Deir Yassin and the Jews.”[22] The view was echoed in a secret Haganah report which stated that the village had stayed “faithful allies of the western [Jerusalem] sector.”[2]”
Deir Yassin had ordered three groups of Arab militants to move off, and they did.
Irgun and Lehi were a nasty lot. Not all the Israelis went so low, but neither did Israel investigate or punish or disavow their terrorists to any degree.