1. Create a custom field with a choice type. I tested with the Checkboxes and the Select List (single choice) type fields. I tested this issue with a Text Field type (multi line), and it didn't work.
2. Set the field up to use only certain Issue Types. Just make sure that the type you choose also has the same type included in your CSV file. My field type utilized the Bug Issue Type. I tested with one, two, and three different types chosen at once. I reproduced each time.
3. Have a CSV file with all the necessary fields to achieve an import cleanly. Just make sure there's a column for the custom field you just created.
4. Map the fields.
5. Instead of choosing the "Begin Import" button, you can choose "Validate".
6. When you do, you should receive an error like this one:

   Cannot add custom field value: null
   The value [ {null=CustomValue} ] can't be added to the Custom Field [ CustomField ]. The value [ {null=CustomValue} ] can't be found or is in the incorrect format
   

Workaround:
Instead of choosing an Issue Type for the field configuration scheme when you configure the field, choose "Any issue type".