What are some Naturalist examples that demonstrate how Blanche, Stella, and Stanley are trapped by circumstance, genetics, and environment?I am...

I would venture to say that part of your challenge is that
it is difficult to link Williams' work to naturalist ideas.  Take this fundamental
description of Naturalism:  "Naturalist writers believe that truth is found in nature,
and because nature operates within consistent principles, patterns, and rules, truth is
consistent."  If we apply this to Williams' depiction in Streetcar,
we can see that not much of this is present.  There is little structure to the world
that embraces Stanley, Blanche, or Stella.  If there were objective rules and
structures, it would be easier for these characters to function.  The challenge that
Williams brings out is the idea that the modern setting is one where freedom is the only
absolute.  Yet, with individual conceptions of freedom comes ambiguity, uncertainty, and
doubt.  These ideas are the diametric opposition to scientific patterns and rules.  We
could use the ideas you pose, though, to help explain some of the characters'
motivations.  For example, Blanche is trapped by her own genetic background in being a
belle from the "old South."  This crushes her because she is incapable of being able to
adapt to how the new South functions.  Stella's environment has had profound effects on
her character in that she has become more pragmatic and practical concerning life and
how it is led.  Finally, I would say that Stanley is a product of his circumstance, a
setting where white men find themselves having considerable more power than others
around them.  It is this power that enables him to rape Blanche and not endure social
repudiation for his actions.  In this light, we can apply principles found in Naturalism
to Williams' work.  Yet, I think that there might be some challenges in trying to assert
that Streetcar is a naturalist work.