Is it important to differentiate between "author" and "speaker" when reading poetry? why or why not?

The
difference between author and speaker in poetry is, in fact, essential to the creative writing
process authors use. Authors don't generally create poems as themselves--even highly personal,
lyric poems.  Authors naturally create a persona and write from a persona's point of view.  The
persona may be similar or different from the writer, but either way it is a persona. 

Most of the time, the creation of a persona is a necessity, and natural to the writing
process.  Poems are highly artificial, even though spontaneity in appearance may be the goal. 
Endless decisions go into the writing of a poem.  The writer starts with the countless material
that could go into a poem, narrows it down and rearranges the raw material into a work of art. 
This must be done from an extremely narrow point of view, or the poem will never end.  This
narrow, limited point of view is the persona.  The persona may be one, narrow part of the
writer's personality, but it is still only one part.  Of course, the persona may not reflect the
writer at all, either, but instead be an exploration unrelated to the writer's own
personality.

Often, this is obvious, and you probably differentiate between
the author and writer more than you think.  You wouldn't read the anonymous
Beowulf  and assume the writer really witnessed the story, would you?  The
poem is a creation, a work of art. 

No one assumes T. S. Eliot is the speaker
of "The Love Song of J. Alfred Prufrock."  Prufrock is the speaker of his love song. 
The narrative is fictional, not autobiographical (though, of course, it may contain
autobiographical elements). 

One can't read poetry and assume everything in
it is actual or real, autobiographical.  Most isn't.  Poems are highly artificial artistic
creations. 

Perhaps, the intensely lyrical (personal) romantic poets might
provide you with a starting place if you want to study poetry in which little separation exists
between the author and speaker.  Perhaps.  Certainly Wordsworth's "Tintern Abbey"
purports to be autobiographical, and may come as close to being so as any poem.  Yet, it is a
highly polished work of art fully "arranged" by the artist.  Strictly speaking, one
would say Wordsworth is the speaker of his poem.  Yet, as a critic, you should possess a healthy
skepticism regarding the poem.  The order of events, the interpretation of events, the slant the
events are given, etc., should not necessarily be accepted as anything other than a work of
art.  In other words, the acceptance of an author as the speaker doesn't mean everything in the
poem is real or actual.   

Finally, the failure to recognize that a writer is
not necessarily the speaker in a poem can lead to misinterpretation.  You ask if it's important
to differentiate.  Yes.  If there is no difference, the freedom to explore an idea a writer
doesn't agree with is taken away from that writer.   Sophisticated literature reveals human
existence, but it can't do that if every idea that appears in a work of art is attributed to the
writer by readers.