I guess you are using FPOS with Google services, thus your default (and only) calendar app is Google calendar, which is forcing you to have a Google account for using it, right? Common “don’t be evil” Google behaviour [/sarcasm]
If Offline Calendar from F-Droid (which doesn’t require any account to fully work, by the way) doesn’t do the trick, you can try another Calendar app which doesn’t force you to register any account, like Standalone Calendar or the material designed Etar.
PD: If you are not using Google apps… have you considered migrating to FP Open OS?