Activity Types access is tied into the user role assigned to someone's profile. If someone is unable to create a reservation with a specific activity type, you will want to make that activity type available for their user role. To do this, click Settings>Users>Roles & Permissions:
Here you will find a list of all user roles available in your company. Next, select Edit next to the user role you for which you want the activity type to be bookable:
Then click on the preferences tab on the top of the pop up window:
You will then see a list of Activity Types with checkboxes next to them. Check the box next to the activity type you want to add to that user role's booking access:
Don't forget to save your changes!
The customer will now be able to create reservations under the desired activity type.