To judge from the dinner party, the Time Traveller has a wide circle of friends, which includes scientific folks, a politician, and several jerks. We learn very little about these characters, who are basically stock figures that represent a cross-section of middle- to upper-class men in 1890s England. There's some science (the Medical Man and the Psychologist), some ignorance of science (the Provincial Mayor) and even some hostility toward it (Filby, the Editor, and the Journalist). One character that's noticeably missing is someone to represent religion. What do you make of this omission, and what are figures like the Silent Man or the Very Young Man supposed to represent?
The dinner guests are all united by one thing: none of them (except the narrator) believe the Time Traveller. In their skepticism, they provide a range of responses to the Time Traveller's story, from the mocking Editor to the concerned Medical Man, who thinks the Time Traveller is suffering from overwork and possibly hallucinated the whole thing (12.24).