They call their god Allah
You say so, you might even believe it. But it is highly misinformed according to many Muslims I know, and also according to a much more popular interpretation of "La ilaha illillah". Allah is NOT god.
That doesn't cancel out and make all of them non-religious groups.
I am not saying that by cancelling they become non-religious. Each individual religious group remains religious.
I am saying that popular disbelief* of Muslims in god makes belief in god wrong. And popular disbelief in Allah by Christians makes Allah wrong according the the wisdom of the crowds.
And by disbelief I don't mean merely indifference. If it were merely indifference, it would not cancel the other group's belief. But they are warned strongly against "false gods" in their gospels and by leaders. I mean active disbelief and denial.