Set a custom registration field for PMPro Register Helper as readonly on the profile edit page.

readonly-on-profile-page-registration-field.php

<?php
/**
 * Readonly field on profile edit page.
 *
 * Add profile_readonly to field and set to true.
 *
 * Fields with this option will remain editable if the field is empty, or
 * if the current user can manage options (administrators), or
 * if the current user is a membership manager that have a
 * membership manager role.
 *
 * Note: This will override the readonly option set for a field.
 *
 * @requires Register Helper Add On
 * @link https://www.paidmembershipspro.com/add-ons/pmpro-register-helper-add-checkout-and-profile-fields/
 *
 * 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/
 */
// We have to put everything in a function called on init, so we are sure Register Helper is loaded.
function my_pmprorh_init_profile_read_only() {
	// Don't break if Register Helper is not loaded.
	if ( ! function_exists( 'pmprorh_add_registration_field' ) ) {
		return false;
	}

	// Define the fields.
	$fields = array();

	$fields[] = new PMProRH_Field(
		'example_readonly', // input name, will also be used as meta key
		'text', // type of field
		array(
			'label'            => 'Example Read Only', // custom field label
			'profile'          => true, // show in user profile
			'profile_readonly' => true, // readonly on user profile edit page
			'readonly'         => true,
			'required'         => true, // make this field required
			'addmember'        => true, // shows on Admin Add Member page
			'memberslistcsv'   => true, // include when using export members to csv
		)
	);

	// Add the fields into a new checkout_boxes are of the checkout page.
	foreach ( $fields as $field ) {

		// Set readonly status on profile if profile_readonly was set to true.
		global $current_user;
		if ( ( $field->profile || $field->attr['profile'] ) ) {
			if ( ( $field->profile_readonly || $field->attr['profile_readonly'] ) && ( empty( get_user_meta( $current_user->ID, $field->meta_key, true ) ) || current_user_can( 'manage_options' ) || current_user_can( 'pmpro_membership_manager' ) ) ) {
				$field->readonly         = false;
				$field->attr['readonly'] = false;
			} else {
				$field->readonly         = true;
				$field->attr['readonly'] = true;
			}
		}

		// Add the fields
		pmprorh_add_registration_field(
			'checkout_boxes',               // location on checkout page
			$field                          // PMProRH_Field object
		);
	}
	unset( $field );

	// That's it. See the PMPro Register Helper readme for more information and examples.
}
add_action( 'init', 'my_pmprorh_init_profile_read_only' );