Despite being invisible in EA desktop app, people still see me online in Apex

@RainyAnt That's interesting, I just tested locally and I was correctly uninvitable on 2 accounts.

Hopefully we can figure out why you aren't properly offline on yours.
Can I check if the people inviting reaching out to you are console players, or PC, or both?

If you haven't done so recently, can you try power cycling your router? Perhaps there's something going on with the router cache and the token that says "show me offline" isn't being properly delivered.