Conditional to see if an Entries field in a user profile contains a certain entry ID
My initial though was that you do not need to not put the "entry.id" in quotes because it's a variable reference, but the contains() method appear to not work as expected here even when this was corrected.

The booksField returns an ElementCriteriaModel, so you should be able to fetch the list of IDs as a plain array and then use Twig's in "containment operator" to search it:

{{ entry.title }}

{% if entry.id in currentUser.booksField.ids() %}
  I have read this book
{% else %}
  I haven't read this book
{% endif %}