radical islam terrorism doesn't bunch people together though? By pointing out that it's radical it shows it's particularly exceptional part of the religion and not the norm?
So yeah. Call it radical islamic terrorism.
Except in the context of American politics and in her use of it, that was clearly not the message.
This was a very popular talking point for years among the Fox News set: Obama avoided using the words "radical Islam" because he was protecting Muslims at the expense of the US, and not acknowledging that Islam itself was a problem. This was all very explicit and widespread, and I'm surprised you didn't encounter this during your conservative Rumspringa.
edit: as analogy, Hannity or whoever ranting about "radical socialists"
could be interpreted as differentiating between them and the acceptable socdems/left-liberals, but we all know that's not the game.