See three related feature requests to address the issue of users agreeing when they should not:
https://forum.inaturalist.org/t/add-extra-confirmation-step-when-agreeing-with-ids-on-own-observations/6316 (still open)
https://forum.inaturalist.org/t/limit-available-agree-buttons-specifically-in-the-activity-feed/6574 (closed)
I’m not sure if there’s an existing request to just remove the agree button on user’s own observations, but not otherwise prevent user’s adding that ID, though this option has definitely been discussed.