Tests break when they are running in parallel

When I run features in parallel (by setting maxInstances to 2 in wdio.conf.js) they fail every other time, but when maxInstances is 1, everything works just fine. It seems that those two tests use sessions of each other somehow when they are run in parallel. Any idea what it can be?

One important thing. Webdriver.io fails to do the assertions (since they are made on different sessions somehow), so the stacktrace is pretty straightforward for a failed assertion.

wdio.conf.js

exports.config = {
  specs: [
    './features/*.feature'
  ],
  maxInstances: 2,
  services: ['selenium-standalone'],
  capabilities: [
    { browserName: 'chrome' }
  ],
  baseUrl: 'http://localhost:4000',
  framework: 'cucumber',
  reporters: ['spec'],
  cucumberOpts: {
    require: ['./features/steps.js'],
    strict: true
  }
};

login.feature

Feature: Login page
  Scenario: Click on the search link redirects the user
    Given the user is on the login route
    When the user clicks on the search link
    Then he sees the search route

search.feature

Feature: Search page
  Scenario: Click on the login link redirects the user
    Given the user is on the search route
    When the user clicks on the login link
    Then he sees the login route

steps.js

const { Given, When, Then, Before, After } = require('cucumber');
const { assert } = require('chai');

Given(/^the user is on the login route$/, () => browser.url('/login'));
When(/^the user clicks on the search link$/, () => browser.click('.search-link'));
Then(/^he sees the search route$/, () => assert.equal(browser.isExisting('.search-route'), true));

Given(/^the user is on the search route$/, () => browser.url('/search'));
When(/^the user clicks on the login link$/, () => browser.click('.login-link'));
Then(/^he sees the login route$/, () => assert.equal(browser.isExisting('.login-route'), true));