Thank you for posting this in Microsoft Q&A.
I understand you trying to add members to a security group, but the "Add member" option is grayed out in Microsoft Entra admin center as like below image.
One reason is to lack of permissions. Could confirm which admin role you have assigned to user?
In order to create , edit groups into Microsoft Entra admin center user must have one of the following roles: Groups Administrator, User Administrator, Privileged Role Administrator, or Global Administrator
Second reason, some groups can't be managed in the Microsoft Entra admin center
- Groups synced from on-premises Active Directory can be managed only in on-premises Active Directory.
- Distribution lists and mail-enabled security groups are managed only in Exchange admin center or Microsoft 365 admin center. You must sign in to Exchange admin center or Microsoft 365 admin center to manage these groups.
Hope this helps. Do let us know if you any further queries.
Thanks,
Navya