You can find a lot of writing that theorizes about Plath's deeply personal connections to the speakers of her poems, with "Mushrooms" being no exception. For example, there's been a lot of talk over the years about Sylvia Plath's rocky marriage to fellow poet Ted Hughes. Some have even gone so far as to blame him, in part, for Plath's suicide, as he had left her for another woman when this occurred. He's been painted as the kind of misogynistic guy that "Mushrooms" seems to be gunning for. We're in no place to judge the guy, but a lot of folks have made this connection. Many have also talked about Plath's frustration at not being taken as seriously as some of male poets because she was a woman. Like the mushrooms, she may have felt left in shadows by both her husband and the poetic community as a whole.
All that said, it's hardly ever a good idea think of the poet as the speaker. For example, we're pretty sure that Sylvia Plath was not a mushroom. The speaker of the poem speaks from the perspective of these frustrated fungi, and seems to use them to symbolize the whole of the oppressed group of which she's a part.
So, in that sense the speaker is kind of a spokesperson for this mushroom underclass. Or, in another sense, you could also interpret the poem as having more than one speaker. It's almost as if we're hearing a chorus of voices describe their quiet, yet determined revolution. Notice, the uses of "we" and "our" in the following passage:
Nudgers and shovers
In spite of ourselves.
Our kind multiplies:
We shall by morning
Inherit the earth.
Our foot's in the door. (28-33)
You could choose to see this as the voices of millions of speakers, all declaring their frustration at their place in the world and the inevitability of their rise.