The pattern:
When specific members of the Other Group display reprehensible behavior, they are cited as evidence that the Other Group as a whole is reprehensible.
When specific members of My Group display reprehensible behavior, they are dismissed as outliers who do not represent My Group as a whole.
The second part is clearly the No True Scotsman fallacy, and the first one is just a basic generalization. I was wondering if there was a name for this specific (and very frequently used) combination.