Custom tags can only be viewed and edited by Account Owners or those with Administrator permissions.
Beamible tags can be viewed by Account Owners or those with Administrator Permissions, however they cannot be edited or deleted.
If you don't want your organisation to use the Beamible tags, you can 'disable' them by going into the 'Tags' tab and clicking on the 'eye' to the far right of the relevant tag. This will remove it from the Activity tag drop down list in the design.
You can always 'enable' it at a later time by clicking on the 'eye' again within the 'Tags' tab.