To be מוחה to object to evil even when you will not be listened to I heard from Leibel (the son of Rav Shmuel Berenbaum [the head of the Mir in NY.]). 

He was saying this to me in terms of the Eruv issues that came up then. [What counts as an enclosure for the Sabbath Day.] I had asked something along those lines. He said that there is a point to object.

Now as I think about it I recall that you can see this with the war between Israel and the tribe of Benjamin. פילגש בגבעה. Look at the verses and you will see the main objection was not what was done the the concubine--which was horrible in itself. Rather the major issue was that no one objected. Israel had gone to the town and asked the criminal to be handed over. And that is the point. Everyone in Benjamin went along with it and no one objected.

Also in the incident of Kamtza and Bar Kamtza. What was done was evil. But that in itself was not enough to bring about the destruction of the Temple, The main issue was that מדלא מחו שמע מינה דניחא להו--that no one of the sages objected.

This would be the same reason that the Gra put his signature of the letter of excommunication. To object to evil even if one will not be listened to. [Just to be clear the actual "herem" did not include Rav Nahman of Uman]. One could look up the books that contain  all the letters and testimony in Villna to see this.