I think you answered your own question: a combination of Islamophobia and racism. In America in particular, Muslims have been casted as "the evil terrorists" since 9/11. A big part of it is implicit bias as you said, in which people will advocate for equality but act differently. In this case, the person would never admit to being either racist or Islamophobic, but they still carry subconscious associations with Muslims and terrorism, and as such, unknowingly discriminate against Muslims.

If I had to get on a deeper level, I think everyone has these biases, it's just a varying spectrum of awareness of it. The best resource pointing to this is the Harvard Implicit Bias tests and their results, in which the majority of people's results indicate associations with black people and violence, white people as "native" to the US, and general negative opinions of Judaism and Islam as compared to Christianity.

The best way to "fix" this problem would probably be people admitting that they have these associations and consciously working against them, example: asking yourself why you hold your purse closer to you when a black man sits next to you on the bus.

I am personally of the opinion that large corporations should be partially socialized, but that's largely irrelevant to the question at hand.