Your family history data is stored exclusively in your own WordPress database. Full GEDCOM export is included in the free version - take your complete data to any genealogy application, at any time, from the Import / Export tab.

Nothing is transmitted anywhere by the genealogy features. The only optional services that can receive limited non-genealogical information are Freemius (licensing and checkout, only if you opt in or buy a licence) and the optional support service behind the Help assistant - both itemised under External services on the plugin's WordPress.org page, and neither is required.