But, he'll still share and talk quite hateful things towards them. I
know deep down it isn't because he genuinely has a hatred for Muslims,
it's because he's believing the lies that he's reading.
This is no different from saying that ISIS members don't have a "genuine hatred" for the West, they just believe the lies they hear from other extremists.
NO reasonable person can believe the sort of lies that justify fear and hatred towards a large and incredibly diverse group of people, most of whom are kind and peaceful. I think it is more accurate to say that the emotions of fear and hate draw people to the sorts of lies that justify the fear and hate that they already have in their heart.
Why do people have that fear and hate in the first place? It comes from a very primitive place in the human psyche: an in-group vs. out-group instinct that says "people like me are good, people who are not like me are bad". From an evolutionary perspective, it is easy to see how this mentality is adaptive in a context where people live in small social units that must compete against other units for resources and survival. The more people feel that the survival of their group is somehow threatened, the stronger these tribal instincts become.
In my experience, people can change and recover from hate, but the only way to do this is by appealing to the same in-group vs. out-group instinct that leads to hate in the first place. The key is for that person to feel as if members of the "out-group" are now in their "in-group", which shatters the divide that they previously held in their mind. You mentioned in the comments that you and Bob don't have Muslim friends in your circle, which is not surprising at all. If Bob was actually friends with Muslims, and felt that some Muslims are in his in-group because they share many of his interests, values, humor, etc., it would become impossible for him to hate "Muslims" in general, and he would be forced to develop a more nuanced view on what it means to be Muslim.
I have had this experience many times in my life with homophobic people. I grew up in a very homophobic environment, including my immediate family and many friends growing up. Long before they knew I was gay, I used to argue with them about their homophobic views using facts, logic, science, etc. I thought that if I could just come up with the perfect, irrefutable argument, then I could change their minds. But it never worked out that way. It seemed like my arguments would only entrench them further in their views, as they would find their own dubious "science" and "facts" to support the idea that gay people are disgusting, unnatural, perverted, immoral, and harmful to society. It wasn't until I returned home as an adult and started saying two simple words, "I'm gay", that the vast majority of people I was close to actually changed their views on homosexuality completely. I have even heard some of these former homophobes standing up for LGBT people when they hear negative comments in their wider social circle, and it is all because when they think of gay people now, they don't think of some scary imaginary weirdos out there in the world threatening their sense of normalcy- instead, they think of ME, a normal person in their in-group who they care about. Thus, the same in-group vs. out-group instincts that made them hateful towards LGBT people in the past have now made them protective towards LGBT people.
All of this can be difficult to accept if you are a very logical person (like myself), but the key to understanding hate is to realize that hate is never based on facts and logic; hate is rooted in primal emotions, and it seeks out fake facts and bad logic to justify its own existence. The only way to change primal emotions is to appeal to even stronger primal emotions. By bringing someone from the "out-group" into the "in-group", a hateful person can become a defender of the group they used to hate. It isn't guaranteed to work, and it is important to recognize that this may take time and patience. It requires a real emotional connection to be established, and that can be difficult, particularly when Bob's attitudes could easily alienate potential Muslim friends. But in my experience, this is the only way to really change people who have hate in their heart. Arguing will likely entrench their views as they increasingly draw on the bottomless pit of bad information available on the internet, and trying to shame them or punish them for their views might lead them to suppress their views in public without actually changing them.
In terms of what YOU can do in the immediate situation, it should be clear by now that I don't think there is a quick and easy answer. It may be that there is not much you can do besides being patient, sharing your experiences, setting a good example, and hoping that Bob eventually has an experience that changes him. But if your goal is to help Bob change, I don't think that arguing endlessly or treating him with meanness is productive.
For further reading on this, reading the stories of reformed white supremacists is really helpful, and there is a lot of material out there (just Google, e.g., "reforming white supremacists"). There are also entire organizations dedicated to reforming members of hateful groups, e.g., Klansmen, neo-Nazis, etc. These are obviously extreme cases, but hate is hate, and it comes from the same place, so you might get some insight from these cases.