You should be able to use the Feeds page (https://micro.blog/account/feeds) to achieve this. If all of your posts are in distinct categories, and you have a birding category, you can remove you default feed and add each individual category feed, but not the birding category feed. But you would need to make sure all posts were assigned a category, and also I assume it would double post if you had two categories assigned to a post, etc.
Working out what your feeds are called is explained elsewhere in help.
This does not make the posts truly private, but there would be no public links to the posts - you could bookmark the category list page for personal access.