Face covering exemption cards exist only for the confidence of the wearer, and are not a legal requirement. Indeed, no person is required to disclose personal medical information in order to gain access to their essential daily services, and to be treated with respect when doing so.
Do ensure your managers and staff are reminded of their obligations under the Equality Act 2010 to provide reasonable access to services for disabled people, including providing reasonable adjustments where necessary to allow them to access their essential needs.
Please be aware of this recent case - believed to be the first in the UK - unlikely the last.