Corporations in general have the constitutional protections that people acting in a group have. Corporate personhood is just a convenient legal fiction.

For example corporations don't have a right to free speech because they are "persons" but because we extend the rights of the individuals who make up the group to the group itself.

> we extend the rights

The constitutional basis for that is not secure.

It's not obvious that your right to free speech extends to secretly paying someone else to speak.

If I leave an iPod in a public park playing a speech, the authorities can remove or disable the iPod, not a violation of my speech rights.

I'm pretty sure they can also remove you; what they can't do is remove you based on the content of your speech, but then again I doubt they can have a policy of only removing iPods playing political speeches with certain viewpoints.