ACL in Joomla have some rules. Problem is that you probably denied access for Public usergroup. Then all other usergroups will inherate this settings and you are not able to change it.
See Joomla Permissions rules (highlighted an important part):
1. If you change the setting, it will apply to this and all child groups, components and content. Note that:
Inherited means that the permissions from the parent group will be used.
Denied means that no matter what the parent group's setting is, the group being edited cannot take this action.
Allowed means that the group being edited will be able to take this action
(but if this is in conflict with the parent group it will have no impact; a conflict will be indicated by Not Allowed (Locked) under Calculated Settings).
Not Set is used only for the Public group in global configuration. The Public group is the parent of all other groups. If a permission is not set, it is treated as deny but can be changed for child groups, components, categories and items.
2. If you select a new setting, click Save to refresh the calculated settings.
For this reason do not denie it for Public usergroup, but use Booking settings to disable reservations for non-registered users.
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