Set a custom date format for the PMPro email date related variables that overrides the site's default date format.

date-format-for-pmpro-email-variables.php

<?php
/**
 * Set a custom date format for some PMPro date email data variables.
 *
 * Set your custom date format in the $date_format variable.
 * See https://www.php.net/manual/en/datetime.format.php for more information.
 *
 * You can add this recipe to your site by creating a custom plugin
 * or using the Code Snippets plugin available for free in the WordPress repository.
 * Read this companion article for step-by-step directions on either method.
 * https://www.paidmembershipspro.com/create-a-plugin-for-pmpro-customizations/
 */

function my_pmpro_email_data_date_format( $data, $email ) {

	global $wpdb;

	// Set your preferred date format.
	$my_date_format = 'd-m-Y';

	// Let's get the user
	$user = get_user_by( 'email', $email->email ) ? get_user_by( 'email', $email->email ) : $user = get_user_by( 'login', $data['user_login'] );

	// Bail if we don't have a user.
	if ( empty( $user ) ) {
		return $data;
	}

	// Get the user's membership level.
	$level = pmpro_getMembershipLevelForUser( $user->ID );

	// Set custom date format for !!startdate!! variable.
	if ( ! empty( $level->startdate ) ) {
		$data['startdate'] = date_i18n( $my_date_format, $level->startdate );
	} else {
		$data['startdate'] = '';
	}

	// Set custom date format for !!enddate!! variable.
	if ( ! empty( $level->enddate ) ) {
		$data['enddate'] = date_i18n( $my_date_format, $level->enddate );
	} else {
		$data['enddate'] = '';
	}

	// Set custom date format for !!membership_expiration!! variable.
	if ( ! empty( $level->enddate ) ) {
		$data['membership_expiration'] = '<p>' . sprintf( __( 'This membership will expire on %s.', 'paid-memberships-pro' ), date_i18n( $my_date_format, $level->enddate ) ) . "</p>\n";
	} else {
		/* If this is a recurring payment membership let's show them the next payment date. */

		// We want to ping the gateways when we check for the next payment date.
		add_filter( 'pmpro_next_payment', array( 'PMProGateway_paypalexpress', 'pmpro_next_payment' ), 10, 3 );
		add_filter( 'pmpro_next_payment', array( 'PMProGateway_stripe', 'pmpro_next_payment' ), 10, 3 );

		$next_payment = pmpro_next_payment( $user->ID );
		if ( ! empty( $next_payment ) ) {
			$data['membership_expiration'] = '<p>' . sprintf( __( 'Your next payment will be on %s.', 'paid-memberships-pro' ), date_i18n( $my_date_format, $next_payment ) ) . "</p>\n";
		}
	}

	// Set date format for !!invoice_date!! variable.

	$invoice = new MemberOrder();

	$order_id = $wpdb->get_var( $wpdb->prepare( "SELECT id FROM $wpdb->pmpro_membership_orders WHERE user_id = %d ORDER BY timestamp DESC LIMIT 1", $user->ID ) );
	$invoice->getMemberOrderByID( $order_id );

	if ( isset( $data['invoice_date'] ) && ! empty( $data['invoice_date'] ) ) {
		$data['invoice_date'] = date_i18n( $my_date_format, $invoice->timestamp );
	}

	return $data;
}
add_filter( 'pmpro_email_data', 'my_pmpro_email_data_date_format', 10, 2 );