In the Season 3, they (the Brotherhood Without Banners) goals is to protect the smallfolk from any force preying on them, regardless of which King or Lord they support.
In Season 6, they killed a whole group.
One reason could be that they had different religion. But is that the only reason for it?
I like to believe that this group may be different from the one Arya encountered. Or maybe since they are an army, they may have deployed small group of members to different parts of the continent to revolt against the nobles. And since they were not directly lead by Beric and Thoros, they seems to have lost its cause.
Is there only one group of the Brotherhood Without Banners, or maybe there is many?