A very good question.
Personally, I don't consider 'corporations' to be 'people', no.
But in the context of this conversation, does it really matter?
Should not confederations of people deserve to exercise their free speech rights? Do we not also guarantee the right to free association?
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."
After all, this conversation is about the First Amendment, after all.
Do you believe that Exxon, or should I say its multiple investors, have no First Amendment rights?