Hey, in Wix Groups it’s not possible to add a member with private profile. Please, make sure that member you want to add is having a public profile. You can find more info here - https://support.wix.com/en/article/wix-groups-member-privacy-settings-for-groups.
Btw, there is an option you can enable to make all new sign-ups to have a public profile by default. Hope it helps 