Is it normal for my apple wallet to ask for my social security to verify my identity

Yes. See the following from Identity verification for Apple Card or Apple Cash - Apple Support

Apple Cash services are provided by Green Dot Bank, Member FDIC, a regulated financial institution. Green Dot Bank is required by federal law to verify the identity of its customers.

To verify your identity, Green Dot Bank will request Social Security numbers and other personal information to ensure that customers are eligible to use the service.