Ahl Kitaab/mushrik
Yes but we are criticising the view that it was for the specific reason of them ‘not taking shirk as a religion’. When the shirk was clear on them they knowingly did it. God knows what was in their hearts and did hujjah on them- a mushrik is someone who knowingly does shirk. So it seems rather that the differentiating in calling them another name was simply to differ in addresses when revealing the Quran or for us to have clarity of who is being referred to