They are different platforms, so you can’t. If you remove ActivityPub from one Lemmy instance (or server), it would be just one centralized Reddit clone. What makes them special is that every public activity (like, comment, post, etc.) are all sent to other servers in the whitelist. This causes the other instances to also have the same content (copy), making the fediverse possible. Just because you can comment on your instance and that being displayed on some Mastodon instance does not mean you have another account there. Your comment was simply copied to that other Mastodon instance using the ActivityPub protocol.
If you want this so you can claim your comments, posts, likes, etc. on other federated platforms (e.g. Lemmy -> Mastodon), you can look into DIDs. DIDs allow users to have Decentralized IDentifiers. Which means the identity that your content are linked to is not locked into one instance. You can log in with your DID(s) anywhere that supports them.
The thing is that DIDs are still being discussed (or had been discussed) to decide how it would be implemented into ActivityPub. Bluesky, for example, uses DIDs. Which is why you can claim the ownership of your content from one instance on another. Do note that Bluesky does not use ActivityPub, but their own protocol called the AT protocol (which, in my opinion, just exists because they want to be different).