If you want to keep using google playstore and services, you no longer will be able to use f-droid, whether google or any aosp rom. grapheneOS claims it won't be affected given their sandboxed google play and services. Though I'm not sure if eventually google would come up with a counter measure or it won't ever care. They want to enforce that if anyone uses their proprietary stuff the apps interacting with it must be from register developers, which automatically exclude any libre/free app storage on which developers don't want to register to google. GrepheneOS being the exception.

If you use microG with any custom rom, I guess that might work through fake registrations, but can't be sure. But any custom rom without google play and services is supposed to be ok with f-droid. The thing is that google knows most if not all users need one app that depends on their stuff, perhaps bank apps, payment apps, and so on...