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...

iirc they are enforcing this on the play services level, using the play protect system. so if you use a custom rom with google play, you are likely cooked too.

that is if the roms don't implement a system to circumvent it.

I've also been confused about this, but this is my take on it.

You're correct that they are making these changes to Android and not AOSP. This means that an OS like Graphene or e/OS/ will still be able to use sideloaded apps and other appstores like F-Droid.

I think the reason everyone is freaking out about this, is that it hurts appstores like F-Droid. It has a chilling effect on apps that are released to alternative app stores and may cause those stores to fail over time, thus killing FOSS apps at the point of distribution.

That said, this is also over my head technically, so I would love if someone more knowledgable could weigh in.