True, but when the government decides to regulate corporations, they have a right to speak, like the individual person does.
You start from the incorrect premise. You assume that non-natural persons, or corporations from here on, have an inherent right to exist. They do not. They are convenient legal fictions, meant to simplify the relationships between allied actors.
Corporations exist exclusively because we the people, through the government, allow them to. The government issues a charter, and thus has the inherent right to regulate them, however it is seen fit. The corporation that is beyond the rule of national law is a relatively new, and dangerous, concept that is sadly propagating because people don't seem to understand that corporations are a legal convenience and have no inherent right to exist.
If the government didn't provide for the corporate charter, people would still be free to associate and to spend money together to produce goods and services. The corporate charter is a convenience that allows more structured laws surrounding the formation, operations, taxation, liability, and dissolution of these alliances of people. It also makes resolving disputes between interested parties a little easier. But because people choose to obtain a corporate charter, for the favorable tax status and liability status, for example, they absolutely are agreeing to be regulated by the chartering entity. And that regulation can, and should, include restrictions on spending money for political purposes, an activity that should be retained exclusively by natural persons. The natural persons who freely entered into such convenient alliances are (and should always remain) free to speak at will.