Then I wouldn’t imagine it matters whether Islam is a religion or an ideology, would it?
Does the law distinguish between "religion" and "ideology"? Should it?
The dictionary defines ideology as
1 : visionary theorizing 2a : a systematic body of concepts esp. about human life or culture b : a manner or the content of thinking characteristic of an individual, group, or culture c : the integrated assertions, theories, and aims that constitute a sociopolitical program
Most religions could qualify as ideologies under one or more of these definitions. Hence, any law which singles out Islam as an ideology could easily be used against Christians, Jews, Hindus, or other groups.