Do they? In my experience, 90% (at least) of the population is totally ignorant about the realities of how their meat got to their plates. Yes, they know it's a dead animal, and yes, they may have some kind of vague sense of what goes on in a slaughterhouse, but that is quite a bit different from actually seeing it.
Even with 25+ years of vegetarian and later vegan living under my belt, I am still profoundly affected by Meat Is Murder (the song). That effect is multiplied live, and even further with the accompanying visuals. I said this in another thread recently, but I don't believe there's some point that a person can reach where they are doing everything "right" when it comes to not eating animals or using animal products. It's a day-to-day thing that requires making conscious choices, and those choices can be made individually by people who have all kinds of dietary habits. Calling yourself a vegan or a vegetarian isn't about achieving perfection, just like being an omnivore does not exclude a person from being capable of opting out of contributing to animal slaughter as often as they feel possible. The labels don't really matter as much as the individual choices do.
It may seem that way, but I cannot count the number of people I have encountered in my life who attribute their vegetarianism or veganism directly to Morrissey. I would venture to guess that he is responsible for more people going down that path in the past 30 years than anyone else.