These are top and recommended social media login extension for Magento 1 & 2.

1) MagePlaza Magento 2 Social Login Extension : This extension is designed for quick login to your Magento 2 store without processing complex register steps. It is absolutely free.
Link: https://www.mageplaza.com/magento-2-social-login-extension/

2) Mage Store Social Login: Available for both magento 1 and 2. Although this is might be quite expensive but this extension works well. Price for magento 1 is $99 and magento 2 is $199
Link: https://www.magestore.com/magento-social-login-extension.html

3) Plumrocket Inc Twitter & Facebook Login: Compatible with magento CE 2.1, This is an extension that is designed to let your customers quickly login or register using facebook account or twitter
Link: https://marketplace.magento.com/plumrocket-module-psloginfree.html

4) MageHit Social Login: With the 7 most popular social networks supported (Facebook, G+, Twitter, Instagram, YouTube, Amazon and Linkedin), Social Login extension for Magento 2 by MageHit supports customers registering their social network accounts to your store. It simplifies the registration process for customers with just one click. Just $59.
Link: https://marketplace.magento.com/magehit-sociallogin.html

If you have any questions about anything I’ve mentioned in this blog post or anything else related to Magento, please feel free to drop me a message at ilyas.muy@gmail.com. I am Magento Certified Developer with over 5 years experience.

I'd like to recommend top 5 best social media login extensions for Magento 2.
1, Landofcoder Magento 2 Social Login: The extension offers you quick Ajax login, 25+ most popular social networks, multiple style and pre-made template.
View detail: https://landofcoder.com/magento-2-social-login.html/
2, Mageplaza Magento 2 Social Login: The extension is designed for quick login to your Magento 2 store without processing complex register steps.
View detail: https://www.mageplaza.com/magento-2-social-login-extension/
3, BssCommerce Magento 2 Social Login: The extension allows customer to log in Magento site through social media accounts like Facebook, Twitter, Google Plus…
View detail: https://bsscommerce.com/magento2-ajax-social-login-extension.html
4, Aheadworks Magento 2 Social Login: The extension provides a registration shortcut by allowing customers to login via social network accounts.
View detail: https://ecommerce.aheadworks.com/magento-2-extensions/social-login/
5, Webkul Magento 2 Social Login: The extension allows users to sign up into their site using social networks like Facebook, Twitter, Google, LinkedIn and Instagram.
View detail: https://store.webkul.com/magento2-social-login.html
Hope that you can choose the best magento 2 social login extension for your e-commerce site.

I think you have missed 1 more magento 2 social login extension provider see here https://www.mageants.com/social-login-extension-for-magento-2.html