I have inserted the function "do_action( 'social_connect_form' );" in the code of a plugin and it shows the buttons correctly, but when I click on any of the buttons nothing happens.
So I didn't add it to the theme but to a plugin function (a shortcode function). Do you know why your function doesn't work in there?
If I go to the WP login page they show under the login form and they work as expected.
Here where they don't work:
Here where they work:
If you check it out and find that everything works then it mean I probably found the solution in the meantinme.