How is the film Invasion of the Body Snatchers a reflection of American concerns with communist subversion?

To answer this, just look at the plot of the film.  You
have good Americans who are replaced by people who look just like them but who are
actually aliens.  This can be seen as a metaphor for what many Americans feared that
communists could do.

In those days, there were fears that
anyone could be a communist.  McCarthyism fed this fear--if there could be that many
communists in the government, who might not be a communist?  You would never be able to
tell.  This is just like what happens in the film.  In the film, it is impossible to
really tell the pod people from the regular people, just as it was seen as impossible to
tell a communist from a "good American."  In the film, the pod people are gradually
infiltrating and changing people.  This was what people thought the communists could
do.  They worried that the communists would secretly infiltrate and then start turning
other people into communists without anyone knowing it.

In
this way, the film reflects the concerns that people had--it reflects the fear that the
communists could covertly subvert the whole country, turning good Americans into
reds.