To make SharePoint Designer 2013 use modern authentication, I added the following registry key to my Windows 10 machine.
Registry key: HKEY_CURRENT_USER\Software\Microsoft\Office\15.0\Common\Identity
Type: REG_DWORD
Name: EnableADAL
Value: 1
After making the registry change, I re-opened SharePoint Designer 2013 and was able to connect to the site collection successfully.
