I'm not a lawyer, but I can offer some general guidance that might help you in this situation. If you believe the affordable housing agency is requesting excessive or unnecessary personal information, and you are uncomfortable providing it, here are a few points to consider:

1. Privacy Concerns: Explain to the agency that you have legitimate concerns about sharing certain financial information, especially when it comes to retirement accounts. Emphasize the importance of protecting your personal and financial privacy.

2. Legal Requirements: Research the local laws and regulations regarding affordable housing applications in your area. Determine if the agency's request for IRA account information is within their rights or if it goes beyond what is legally required. This information can support your argument for not providing the requested details.

3. Alternative Solutions: Propose alternative ways to verify your financial eligibility for affordable housing. For example, you could offer to provide additional bank statements, tax returns, or alternative income verification documents that don't involve revealing sensitive retirement account information.

4. Seek Legal Advice: If the agency continues to refuse your request and you believe your privacy rights are being violated, you may want to consult with a lawyer who specializes in tenant rights or housing law. They can provide you with specific advice based on the laws in your jurisdiction and help protect your rights.

5. Credit Card Dispute: If the agency refuses to return your deposit and you paid it with a credit card, you could consider disputing the charge with your credit card provider. Explain the situation and provide any supporting documentation to make your case for a refund.