G Suite accounts will only allow access to apps using OAuth. Does this affect BusyCal or BusyContacts?

No it does not, BusyCal and BusyContacts already use OAuth 2.0 to access your Google / G Suite accounts. We don't use or store your Google account passwords.

G Suite accounts will only allow access to apps using OAuth. Password-based access will no longer be supported. Google account password authentication, oAuth 2.0