“Just because it also was used for other pagan deities doesn’t change the fact that it was used also by Arabic Christians and Jews.”
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If they didn’t know better or were in fear of having their heads removed from their bodies if they didn’t, it’s understandable.
Jews and Christians used ‘Allah’ (as it appears also in Arammaic... the prvalent semitic language in the ancient Middle East) BEFORE Islam.
The name of the pagan deity of Mekka was ‘Hubal’. Of course the Arabs called him Allah as he was their god.