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.
It is important. In many poems the speaker is someone different than the author and the difference can be important if one is trying to identify the themes or meanings of the poem. There can be important differences between the voice speaking in a poem and the author, at times authors have even used a female voice, though they are male, or they take on various characteristics for the purpose of the poem that are completely outside those of the author.
The most difficult thing in intuiting the speaker and the differences between the speaker and the author can be that the author does not always explicitly discuss the speaker in order to give the reader all the information they need. Sometimes it is incumbent on the reader to figure out the speaker.