ThreadFreedom of speech debate heats up in France after death threats to 16-year-old girl who called Islam "religion of hate"
You're right that there are a lot of people who sadly can't make this distinction, which is why bigotry so easily festers (and it's why political groups have used this kind of thing to manipulate the masses time and time again - it's easy and works). It takes empathy, maturity and understanding to not do this. Personally, as someone who has experienced an extensive amount of Islamophobia myself, and knows more Muslims than any other group of people (including my entire family), it's very easy for me to not generalise Muslims and to yearn for their safety and well-being despite having issues with Islamic scripture.
But even speaking about other religions, it's easy for me to have the same mindset. My own struggles make it easy for me to empathise with others not like me. Intersectionality is hard, but not an impossible task.