Add HTML5 required attribute to fields on the Member Profile Edit page that has the pmpro_required class assigned.

pmpro-member-profile-edit-add-required-attribute.php

<?php
/**
 * Add HTML5 attribute required to all required PMPro fields on the front end
 * PMPro Member Profile Edit page.
 *
 * 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_profile_edit_add_required_html_attribute() {
	global $pmpro_pages;

	// We only want to do this on the member profile edit page.
	if ( ! is_page( $pmpro_pages['member_profile_edit'] ) ) {
		return;
	}

	// Add JavaScript to the footer that adds the required attribute to al fields with the class pmpro_required.
	?>
	<script>
		[...document.querySelectorAll(".pmpro_required")].forEach(element => { element.setAttribute("required", "required") });
		document.getElementById('user_email').setAttribute("required", "required");
	</script>
	<?php
}
add_action( 'wp_footer', 'my_pmpro_profile_edit_add_required_html_attribute', 20 );