Laurence Fox has some highly questionable views. The 'female' in the audience said that Meghan Markle had been treated badly because of her race, and LF said that it was racist of her to refer to him as a 'white, privileged male', entirely missing the point of what racism actually means. In fact, it was LF who called the woman (can we stop calling her a 'female', please?) a racist, not the other way round.
Having said that, words like 'racist', 'bigot' and so on can describe behaviours, but when they are used to define an individual they become subjective and potentially offensive. It's similar to the difference between saying someone is 'crippled' and calling them 'a cripple', or referring to a 'person of colour' (emphasis on 'person') and to a 'coloured person' (emphasis on colour).