Are there any "CRA" type agencies or other organizations that track US residents by religion?

Factual Questions
1

I had the recent experience of shopping for a gift for someone at a store whose raison d’etre is the selling of items related to the practice of a specific faith tradition that I do not subscribe to personally. I paid the item with a debit card.

I was wondering if my name might now be in a database of suspected followers of that faith.

Are there any “consumer reporting agencies” or any other type of organization that purports to track US residents by their religion?

E.g.: "Your background check came back. In addition to the standard criminal and credit checks, we ran your name against the National Faith Database, and it says you are probably Buddhist. This is a Baptist day-care center, and childcare workers here must subscribe to the statement of faith (explains legal exemption to the discrimination laws). Because of the result of the background check, if you wish to work here, you must provide evidence of your faith in Jesus Christ by either providing notarized statements from your pastor and two other Christians, or by successfully challenging your Buddhist designation with the National Faith Database (hands over appeals disclosure information).

2

There are no credit bureaus that record religious preference, to my knowledge.

That said, your name may now be on a mailing list, and that mailing list may be shared with other companies who are looking for potential customers with the same interests, so you may end up getting a lot of junk mail/spam for religious goods, anyway.

Regarding your employment application to the faith-based daycare center, many of them will ask you about your faith during the application/interview process and ask you to sign a statement of faith when you take the job. They don’t need a credit report to find that information.