You can use the Policy plugin for this.
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Protect the category with group “over18”
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Use the policy plugin to have users confirm they are over 18 with parameter
add-users-to-group="over18"
Anyone who confirms they are over 18 will be added to the group and will be able to access the category.
For making the topic titles visible to people outside the group, you could use the category-lockdown plugin.