Redirect user to the site's homepage after the frontend profile is saved.

my_pmpro_redirect_after_profile_save.php

<?php

// Copy from below here...

/**
 * Redirect user to the site's homepage after the frontend profile is saved.
 * 
 * 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_redirect_after_profile_save() {
	echo( "<script>location.href = '" . home_url() . "'</script>" );
}
add_action( 'pmpro_user_profile_update_errors', 'my_pmpro_redirect_after_profile_save' );