I don't think Islamophobia is rooted in racism; rather racism and Islamophobia are rooted by a deeper worry - the universal fear of the unknown.
It makes sense biologically, early humans survived when they were cautious of new nearby tribes or settlements. New can be dangerous. New is a biological trigger for worry.
However, in our modern society, our primitive brains haven't "updated" our thinking to fit with our rapidly changing environment, where different cultures and ideas become increasingly connected. Perhaps this is the reason why many today suffer with social anxieties, especially when many of them are irrational (yet understandable and commonly acceptable) fears. Fear of public speaking, fear of going outside, fear of socialising...
When 80-year-old Ted from down the street picks up his daily newspaper and sees the words 'Halal', 'Hijab', 'Allah (Swt)' mixed in with negative connotations, he is socially learnt to associate this new = bad, ergo Muslims = bad. It's easy money for social media to create a "common enemy" for clicks and attention, and Muslims just happen to fit the bill. In an alternative universe, the Catholics would have been seen as "new" or "the dangerous enemy". Hell, the Jews were already made the common enemy via propaganda before.
But perhaps I am just being pedantic.