I finally figured out what it was!
Wordpress is installed like this:
http://www.domain.com/wordpress/
But my website is in the root like this:
http://www.domain.com/
Therefore, the cookies were not accessible across the board.
https://wordpress.org/extend/plugins/root-cookie/download/
@netweb Thank you for your response!
I guess then my issue is about it not recognizing users are logged in already, then. I will look more into this!