How can I exclude a user from my site collection in SharePoint Online? He is also in the group,
Everyone except external users.
The problem is that if I remove that group then maybe the permission levels will break for my sites.
This is not supported by SharePoint Online, here is the excerpt from the reply of a Microsoft support:
"it is not feasible to remove SharePoint Online internal users from this group. This group is created by SharePoint Online system by default to contain SharePoint Online internal users. It is used for the scenario when sharing some SharePoint Online contents with all internal users instantly."
Full article can be found on Microsoft Community
When a user is added to Office 365, the user automatically becomes a member of
Everyone except external users. By default, the
Everyone except external users group is added to the
Members group on the SharePoint Team Site. It is automatically assigned a permission level of Contribute. This means all users who are added to Office 365 can view, add, update, and delete items from lists and libraries. If you want to change the permission levels for this group, you can remove it from the Members group and then add it to a group that uses different permissions. For example, you might add the Everyone except external users to the SharePoint Visitors group. This automatically assigns a Read permission level to all users in the Everyone except external users group.
Default SharePoint Groups in SharePoint Online
Now, i think it is bad idea to add Everone group on root level with higher permission, i would rather create different groups and then assign permission to them.