My customer is unable to select a certain activity type when creating a reservation.

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.