That's not the issue here. The SSN is a separate field on the application and people who have supplied SSNs are being asked intrusive and irrelevant questions about their immigration status.

To others - if the bank asked every applicant for their eye color then they'd know statistically that those with blue eyes are more likely to default than brown (or whatever). The fact that the bank can choose who to do business with does not make this a relevant or appropriate question. The fact that 99.9% of the banking industry gets by perfectly well (for these purposes) without asking such questions is proof enough that Barclays has no need.