I wanted to use BCH funds instead of BTC and within minutes I got this (helpful) response from Support:

Thank you for reaching out to us. To change your linked wallet, please do the following:
1.) Visit https://www.coinbase.com/settings/security_settings
2.) Remove Shift Card from the list of Third-Party Applications
3.) Open the Shift mobile app
4.) Navigate to Funding Sources and Add BCH Coinbase
5.) Ensure you select the correct wallet during the process