You are a person if you can be killed.
You are a “legal person” if the State can kill you without violating their process.
Equality of legal persons begins with comparing how difficult it is to execute the process that results in the State killing you without breaking the law and how long that takes. In most cases, it ends there; the quicker it is to kill you without consequence, the “more equal” you are.
When was the last time the State killed a corporation? A church? An algorithm?