The First Amendment says that Congress shall pass no law abridging freedom of speech. If you don’t want “corporations and organizations to pump money into elections,” which is a reasonable sentiment, then amend the Constitution. If you liked the idea of a six year term for the President, would you make the obviously absurd suggestion that Congress enact such a rule in derogation of the plain words of the Constitution?
As to the argument that corporations are not people and are therefore different for purposes of the applicability of the First Amendment, would you have a problem with a statute that prohibited unions from engaging in political advocacy? How about a statute prohibiting political parties from engaging in political advocacy? If you have a problem with either, as I hope you do, then you have no argument on the issue of corporations as ‘people’
The reality is that without the ability to aggregate resources, individuals would have a much tougher time than they already have in exercising their First Amendment rights. You or I might have a different comfort level with a union’s political activism than with that of management, but that has no more relevance to the Constitutional question than the size of mine or your bank account.