@Christopher M. is correct that even in states that cannot discriminate against SEC 8, it is unlikely a voucher holder will meet their standard criteria, and as a result, they would be denied for not meeting the criteria, not because they have a voucher.

I think a better policy is to automatically deny anyone that completed their sentence within the last 3-5 years.

If both of them meet your criteria you're safest off choosing the first one to apply, and your reason for denying the 2nd application is that there was a qualified applicant that was "in-line" before them.

I doubt they would move if you deny the request and I doubt $225 of insulation will make a significant difference in their utility expenses.

Its a crazy circus but I also think if they deny the house when reviewing she is going to try to get her money back. 

If she refuses to do that then I'd deny her application.

I would deny them and I would also report them to HUD, particularly if you have this in writing.

I always practiced that you can not deny a tenant's pet if that said pet was a certified "service animal". 

God forbids, if somethign happens and there is a fire, they insurance company can deny all the claims if they find out that someone was living in the basement. 

None of the CFPB-required disclosures require lenders to disclose what percentage of loans they actually close, and what percent they deny 3 days before scheduled closing after all contingencies have been lifted.