There were then and still are now constitutional rights afforded to natural persons but not juridical persons. There is not some inability to distinguish the two. Look at the ruling that Citizens United overturned: https://en.wikipedia.org/wiki/Austin_v._Michigan_Chamber_of_.... It was very clear that it's fine (and necessary) to restrict corporations in some ways precisely because they are not people.

Perhaps the argument of Citizens United wouldn't have been made if we instead used the terms "Human Shmerg" and "Legal Shmerg", but exactly the same argument could apply to shmergness as to personhood when discussing the rights afforded to shmergs of one kind or another, and the conservatives in the US really want to deregulate everything.