Well... I write both fanfics and short stories.
I have one short story that is published in a book, which contains short stories by multiple authors, and my family members have read that one.
My family doesn't know that I also write fanfics.
And some of the fanfics are stuff that I wouldn't show my parents. (for multiple of reasons)
I feel like some of the stories that I write are more "limited" than the stuff I write in fanfics.
Sounds like I care too much about what my parents would want me to write.
And I feel like they would want me to just write "clean" stories with no cursing or "steamy stuff". (I do know that you can write good stories without that stuff, but still...)
And I feel like my mother would be against me publishing a story that has curse words and stuff.
Even though there have been times when I have written kissing scenes featuring two of my story characters, but I feel like it would be too embarrassing to show my parents.
There are also other reasons, why I feel writing anonymously is easier, but I don't feel like saying why at the moment.
I guess that this is one of the reasons why some authors use pseudonyms.
And I'm sure most authors, who write "embarrassing" books, use pseudonyms for those.
Because of the fact that my country is small and almost an "everyone knows everyone" kind of country, it is probably difficult to publish books anonymously.
I think that there was an author once, who wrote a book, where he was being anonymous, but I think that many people could tell which person wrote it.
I'm rooting for you whatever you decide to do. If publishing anonymously is like dipping your toe in the water and gain confidence, then that's a great way to start.