Invasion of the body snatchers is a poster child for modern sci-fi. the idea that 'martians' didn't have shiny suits and antenna was relatively new at this time and director Don Siegel made this new thing work for him.
the film explores many themes, mainly political in light of the cold war and soviet union Russia. it speaks of man losing his personality, conformity and it was at this time that communism, the fear of everyone being this one same person, almost a new world order, was beginning to seem like an eventual reality.
as explained today, through use of the uncanny, Siegel manages to make something that was so safe and familiar (a pleasant little town where everyone seems to know everyone for some reason) and used it against the viewer to make it into something quite the opposite.
i hope I've understood that right?
despite all of this, when asked in an interview, original writer of the story 'the body snatchers', Jack Finney, and actor Kevin McCarthy both stated that there was no intentional purpose to light any theme of communism or any political view for that matter.
(the thing, seeming a trifle more grotesque in its approach)
The whole body snatching idea has been re-used continually throughout sci-fi and even other things. the matrix, the thing, the Simpson's (big surprise), even zombie flicks are similar that a virus takes over your body. it is a successful idea and is timeless.