I’ve also struggled with this. Although I still don’t really understand what causes the problem, I’ve managed to bypass it, by installing a login redirect plugin and changing the standard login URL from www.yourwebsite.com/wp-login.php to www.yourwebsite.com/login. The plugin I used can be downloaded from https://nl.wordpress.org/plugins/rename-wp-login/, but I’m pretty confident that any login redirection plugin would work.
So, this way you don’t have to edit your functions.php.
This bypasses any default Google reCaptchas, by the way.
I would still love to know what the problem is caused by though.