Why do princesses Eugenie and Beatrice use the title HRH then ? I thought they were also not working members of the Royal Family
At the time of their birth the children of a royal prince were automatically prince or princesses by virtue of their father's role. Children of a royal princess were not, see the Phillips' children. This was changed prior to Princess Charlotte's birth so that children of a royal prince and princess are now equal. This is why Charlotte ranks above Louis in the succession, but Anne ranks below Edward and his offspring. It's not to do with whether they work in royal roles or not.
So Prince Charles, Andrew and Edward's children were automatically titled, but Princess Anne's weren't and could've been granted titles but Anne and her husband refused a title for both the husband and the children.