What can prevent my customers from logging in automatically after they click on the login button?

Creating the account and opening the customer session are separate steps. If the account exists after social login but the customer returns to the shop without being logged in, several points need checking.

1. Complete the login flow. Identify the exact failing step and any message shown in the login window or on return to the shop.
2. Check the domain and session. The flow must return to the correct shop with a consistent URL and preserved session cookies.
3. Check caching if you use it. A page cache, proxy or optimization module can interfere with a session. Have the required exclusions for Social Login and account pages tested in your test environment, following the cache solution’s documentation.

Caching is one possible cause: an exclusion does not systematically resolve every login failure. If the problem persists, send support the module, PHP and PrestaShop versions, the provider used, the test time and an error message stripped of confidential data.

For a Facebook state-check message, see this FAQ.