How to write test(s) with specific config to test custom access checks?
Wound up figuring this out I suppose, although I have no idea if this is the proper way.

Under the custom module I wanted to test, I created a 'tests' directory with a test module and within that new module placed 3 configuration files from my project config ("Show Profile" field storage, "Show Profile" field instance, user form display configuration).

In a functional test, I required that module:

&lt;?php

namespace Drupal\Tests\mymodule\Functional;

use Drupal\Tests\BrowserTestBase;
use Drupal\user\Entity\Role;

/**
 * Class ProfileAccessTest
 * @package Drupal\Tests\mymodule\Functional
 */
class ProfileAccessTest extends BrowserTestBase {

  /**
   * A set of test users.
   */
  protected $user1, $user2, $user3, $user4;

  /**
   * {@inheritdoc}
   */
  protected static $modules = ['node', 'user', 'mymodule', 'system', 'mymodule_test'];

  /**
   * {@inheritdoc}
   */
  protected function setUp() {
    parent::setUp();

    $anon_role = Role::load(Role::ANONYMOUS_ID);
    $this-&gt;grantPermissions($anon_role, ['access user profiles']);

    $this-&gt;user1 = $this-&gt;drupalCreateUser(['access content', 'access user profiles'], 'regular_user');
    $this-&gt;user2 = $this-&gt;drupalCreateUser(['administer users'], 'john', TRUE);
    $this-&gt;user3 = $this-&gt;drupalCreateUser([], 'zzz', FALSE);
    $this-&gt;user4 = $this-&gt;drupalCreateUser([], 'yyy', FALSE);
  }

  public function testProfileAccess() {
    // The average user should not be able to do anything to their own account.
    $this-&gt;drupalLogin($this-&gt;user1);
    $this-&gt;drupalGet('/user/' . $this-&gt;user1-&gt;id());
    $this-&gt;assertResponse(403);
    $this-&gt;drupalGet('/user/' . $this-&gt;user1-&gt;id() . '/edit');
    $this-&gt;assertResponse(403);
    $this-&gt;drupalGet('/user/' . $this-&gt;user1-&gt;id() . '/cancel');
    $this-&gt;assertResponse(403);

    $this-&gt;drupalLogin($this-&gt;user2);
    $this-&gt;drupalGet('user/' . $this-&gt;user3-&gt;id() . '/edit');
    $edit['edit-field-show-profile-value'] = 1;
    $this-&gt;drupalPostForm("user/" . $this-&gt;user3-&gt;id() . "/edit", $edit, t('Save'));

    $this-&gt;drupalGet('user/' . $this-&gt;user4-&gt;id() . '/edit');
    $edit['edit-field-show-profile-value'] = 0;
    $this-&gt;drupalPostForm("user/" . $this-&gt;user4-&gt;id() . "/edit", $edit, t('Save'));

    // Any user should be able to view an account with SHOW PROFILE true.
    $this-&gt;drupalLogin($this-&gt;user1);
    $this-&gt;drupalGet('/user/' . $this-&gt;user3-&gt;id());
    $this-&gt;assertResponse(200);

    // But not if SHOW PROFILE is false.
    $this-&gt;drupalGet('/user/' . $this-&gt;user4-&gt;id());
    $this-&gt;assertResponse(403);
  }
}


The tests all pass, which is good.