ManyRelatedManager object is not iterable

Sounds like you are looking for something like

Store.attribute_answers.all()

If you are doing this in a template:

{% for room in study.room_choice.all %}
  {{ room }}
  {% empty %}
  empty list!
{% endfor %}

UPDATE

If you have a through table, you can access the elements in that table (as detailed here) like so (note, you use the through table name, in lowercase, suffixing _set):

{% for roominfo in participant.roomchoicethru_set.all %}
  {{ roominfo.room}} {{ roominfo.telnumber}}
{% endfor %}

Try

matches = [val for val in Store.attribute_answers.all() if val in WishList.attribute_answers.all()]

Notice the parenthesis at the end of WishList.attribute_answers.all(). Adding the parenthesis invokes the all function to return an iterable.

If you include the parenthesis you're saying "give me all the values in the stores answers so long as that value is also in the wish lists answers". Without the parenthesis you're asking for all the values from the store's answers that are also in the all function, which is meaningless. The all function is not an iterable (it's a function that returns an iterable)