Have members use their email address for logging in to your website powered with Paid Memberships Pro

pmpro-email-as-username.php

<?php // Do not include in PMPro Customizations plugin
/**
 * Have members use their email address for logging in to your website powered with Paid Memberships Pro
 * 
 * Paste the code below into a PMPro Customization Plugin: 
 * https://www.paidmembershipspro.com/create-a-plugin-for-pmpro-customizations/
 */

add_filter( 'gettext', 'wordpress_login_gettext', 20, 3 );
function wordpress_login_gettext( $translated_text, $text, $domain ) {
	if ( 'wp-login.php' === $GLOBALS['pagenow'] ) {
		if ( 'Username or Email Address' == $translated_text ) {
			$translated_text = __( 'Email address' );
		}
	}
	return $translated_text;
}

function pmpro_init_email_as_username() {
	if ( strpos( $_REQUEST['log'], '@' ) !== true ) {
		$no_continue = pmpro_setMessage( 'Your username should be an email address', 'pmpro_error' );
		return false;
	}
}
add_action( 'wp', 'pmpro_init_email_as_username' );

function pmpro_gettext_username_to_email( $translated_text, $text, $domain ) {
	if ( ( 'woocommerce' === $domain || 'pmpro' === $domain || 'paid-memberships-pro' === $domain ) && $text == 'Username or Email Address' ) {
		$translated_text = 'Email address';
	}
	return $translated_text;
}
add_filter( 'gettext', 'my_gettext_username_to_email', 15, 3 );