Currently Apple Card accounts are only accessible via the Apple Wallet app. Unfortunately, we cannot support mobile sites based with iOS access only as of now. Apple Card accounts would need to be updated manually in Banktivity until this changes. If Apple (or Goldman Sachs) decides to allow access to Apple Card account information online from a web browser application, we should then be able to add Direct Access support at that time.
Update 4/17/20: The Banktivity 7.5 update should allow you to import OFX and/or CSV files exported from the Wallet app. The best way to update Banktivity is to go to Banktivity> Check for Updates.
Update 1/1/21: Our Direct Access team is working on adding Direct Access support for Apple Card accounts. We hope support can be added soon, but in the meantime you should be able to export your Apple Card transaction data from the Wallet app on your iPhone and then import the data into Banktivity.