Error when end-users access Contact Dashboard
You have to have this permission (access CiviCRM backend and API) for anyone to access anything CiviCRM related, it's the minimum permission required for anyone to do anything.

You can have a look at some information regarding this here - https://lab.civicrm.org/dev/drupal/issues/45

There are a lot of other pages that say similar things as well, it sounds like a scary permission to give someone but in reality it's more of a first step kind of thing. 

Unfortunately, this means that anyone with the access CiviCRM backend and API permission can see the CiviCRM menu but there are ways of going about this such as the answers on this question - How to remove CIviCRM from menu for some roles