Can a financial institution require an individual to provide their citizenship if it is a secured loan?

Is that not something you can already determine using SSN/ITIN and ID?

"Citizenship?" is the most fundamental due diligence question of all; it does not make any difference what the proposed relationship might be.

Perhaps I don't understand the question. This is clarified on the W-9 form. Is the question whether or not the bank can deny a loan based on citizenship status?

Are you talking about ECOA 1002.6?

Paragraph 6(b)(7)
1. National origin—immigration status. The applicant's immigration status and ties to the community (such as employment and continued residence in the area) could have a bearing on a creditor's ability to obtain repayment. Accordingly, the creditor may consider immigration status and differentiate, for example, between a noncitizen who is a long-time resident with permanent resident status and a noncitizen who is temporarily in this country on a student visa.

2. National origin—citizenship. A denial of credit on the ground that an applicant is not a United States citizen is not per se discrimination based on national origin.

I would look at the collateral. It is not the (usual) intent to liquidate the collateral for repayment, so for collateral that the borrower has control over, it might be more of an issue than (e.g.) a loan secured by a CD held by the bank.

The completion of a W-9 has nothing to do with citizenship.