How to create a free Membership sign-up?
Here's an Example of a clean FREE Membership page with no hint of needing to contribute! On the Contribution Page Config -> Memberships Tab -> make sure you select the Membership.

Note 1: you'll want to add some anti-spam control - like add a reCAPTCHA to a profile that you expose on your Contribution Page

Note 2: In Drupal we can sync Membership Type/Status -> to Drupal role - and can then create Member only content pages. Not sure if you can do that in Wordpress - but that's often our use case for a FREE Membership.