As far as I know, this can not yet be customized. There are ways for removing these sections for the contact record view (right sidebar, under Settings > Objects > Contacts > Record customization), but they don't affect the sidebar in the conversations inbox.
As far as I know, this can not yet be customized. There are ways for removing these sections for the contact record view (right sidebar, under Settings > Objects > Contacts > Record customization), but they don't affect the sidebar in the conversations inbox.