Corporations are obviously not people –they are groups of people who share a common purpose. However an individual does not lose his rights by acting on behalf of a group. The purpose of the group is irrelevant - whether a group exists for the purpose of prayer, or political advocacy, or profit does not change the rights of the people involved.
The attack on “corporate personhood” is an attempt to deny the rights (primarily the freedom of speech) of people working for certain non-politically correct groups – namely groups with the primary purpose of making a profit. This is just a veiled attack on capitalism and property rights.