Why did the Brotherhood Without Banners attack this group in S06E07?

Question

In S03E04 ("And Now His Watch is Ended") of Game of Thrones, Beric Dondarrion says to Sandor Clegane:

That's what we are: ghosts. Waiting for you in the dark. You can't see us, but we see you. No matter whose cloak you wear: Lannister, Stark, Baratheon, you prey on the weak, the Brotherhood Without Banners will hunt you down.

Then why did the Brotherhood Without Banners kill this group of commoners doing building work in S06E07. Did the Brotherhood Without Banners ever do something similar in the books?

Answer 1

As per Season 6 Episode 8, "No One", the members of Brotherhood Without Banners which attacked and killed the villagers and the septon are shown to be a splinter group which did an unsanctioned attack.

The Brotherhood Without Banners' leader, Beric Dondarrion, Thoros of Myr and company were about to hang them (the splinter group) for murdering the villagers, until they met Sandor Clegane. Related dialog:

Thoros: Clegane. What the fuck you doing here?

Clegane: Chasing them. You?

Thoros: Hanging them.

Clegane: Any particular reason?

Beric: They're our men. Or they were.

Beric: They attacked a nearby sept and murdered the villagers.

Beric: Why do you want them?

Clegane: Same reason. I was helping build it.

...

Beric: It's the Brotherhood's good name they've dragged through the dirt.

This shows that the Brotherhood Without Banners have not turned to banditry, don't approve attacking innocents simply because they are of another faith, and they were not specifically targeting the septon or Sandor Clegane.

They also don't see Clegane as an enemy. They believe that Clegane winning the trial by combat against Beric is the Lord of Light's will. They even asked that Clegane join them as they make their move northwards:

Beric: You ought to join us. We could use you.

Clegane: I tried joining. Didn't work out for me.

...

Beric: Cold winds are rising in the North.

Clegane: And you're going to go stop them?

Beric: We need good men to help us.

Clegane: Last time you saw me, you wanted to execute me.

Beric: True enough. But the Lord of Light gave you the power to defeat me.

Answer 2

EDIT: As of S06E08 it would appear that Lem and his two buddies were conducting your basic brigandry and operating without consent of the "official" BWB. Sad to see the writers resorting to essentially Deus Ex Machina to reintroduce Clegane to the plot. Also, bummer that this episode more or less precluded the introduction of LSH.

Possibilities:

Targeting Ray If Ray was a former cutthroat, the BWB might have reason to want him dead, and to kill his followers out of followthrough. This is essentially how they behave in the books after LSH takes over.

Religion The BWB ostensibly follow R'hllor after watching Thoros of Myr resurrect Beric D, and and watching Beric D. resurrect LSH. Ray and his people were building a sept, which could have been provocation enough. Note that this is the primary reason for the attack implied by the "previously on GoT" montage at the beginning of S06E08.

They've Got No Principles and Have Become Outlaws Thoros of Myr states as much about the BWB in book 4, after they come under the leadership of a vengeance-driven LSH. We have a winner. Lem and his two companions appeared to be acting as a plot device to get SC back into the story.

They Recognized Clegane As a former servant of the Lannisters, Clegane and the people he lived with would be prime targets for the BWB. In their eyes, and especially in the eyes of LSH, his newfound thoughtfulness would not absolve him of his prior actions.

Answer 3

I'm not sure I buy any of the possibilities listed above. To start, I'm pretty sure the BWB was already pretty heavy into R'hllor when we first met them. And they weren't attacking practitioners of the Faith of the Seven then; they were targeting Lannister soldiers who were being shitty to the commoners. The original version of the BWB would consider this the exact type of group they WOULDN'T attack.

Whether they recognized Clegane or not, he was "absolved" when he killed Beric Dondarrion in their trial-by-combat. To me, this is definitely pointing to a Lady Stoneheart arc. And even then, the only real reason I can think that they'd attack 'em is the Faith's relatively recent reassociation with House Lannister.