Select2 depends example for Register Helper and Custom JQuery.

my-pmprorh-depends-select2.php

<?php
/**
 * This recipe is an example of how to
 * toggle the display of depending "child" fields
 * when using select2 field types
 * for Register Helper.
 *
 * @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/
 */


function my_pmprorh_init_depends_select2_and_multiselect() {
	//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(
		'select_2_parent', // input field name, used as meta key
		'select2',          // field type
		array(
			'label'   => 'Select2 Parent',
			'options' => array(
				'option_1' => 'Option 1',
				'option_2' => 'Option 2',
				'option_3' => 'Option 3',
			),
		)
	);

	$fields[] = new PMProRH_Field(
		'select_2_child', // input name, will also be used as meta key
		'text', // type of field
		array(
			'label' => 'Select2 Child',
		)
	);

	//add the fields into a new checkout_boxes are of the checkout page
	foreach ( $fields as $field ) {
		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_depends_select2_and_multiselect' );


function add_select2_depends_js_to_footer_example() {
	global $pmpro_pages;

	// Only load script on checkout page.
	if ( is_page( $pmpro_pages['checkout'] ) ) {
		?>
	<script type="text/javascript">
		jQuery(document).ready(function ($) {

			/* Enter your values below */

			// 1. Multiselect or select2 field name here
			var depend_parent_field_name = 'select_2_parent';

			// 2. The value of the option you want to check.
			var depend_value = 'option_3'; // the value of the option you want to check.

			// 3. The name of the field that depends on the parent field
			var depend_child_field_name = 'select_2_child';

			// 4. Set to true to make this depending field required or set to false to make it optional
			var required_field = true;

			/* ************************************************************** */
			/* That's all, you don't need to change anything below this line  */
			/* ************************************************************** */

			// Variables
			var depend_parent = '#' + depend_parent_field_name; // #select_2_parent
			var depend_child = '#' + depend_child_field_name; // #select_2_child
			var depend_child_div = depend_child + '_div'; // #select_2_child_div
			var depend_child_required = depend_child + '_required'; // #select_2_child_required
			var depend_child_span = '<span id="' + depend_child_field_name + '_required" class="pmpro_asterisk"> <abbr title="Required Field">*</abbr></span>';

			// Hide child field
			$(depend_child_div).hide();

			// Add required asterisk
			$(depend_child).after(depend_child_span);

			// Hide required asterisk
			$(depend_child_required).hide();

			// Show fields.
			$(depend_parent).change(function () {

				jQuery.inArray(depend_value, $(this).val()) > -1 ? $(depend_child_div).show() : $(depend_child_div).hide();
				// Optional - Make Required
				if (required_field) {
					jQuery.inArray(depend_value, $(this).val()) > -1 ? $(depend_child).prop('required', true).addClass('pmpro_required') : $(depend_child).prop('required', false).removeClass('pmpro_required');
					jQuery.inArray(depend_value, $(this).val()) > -1 ? $(depend_child_required).show() : $(depend_child_required).hide();
				}
			});
		});

	</script>
		<?php
	}
}
add_action( 'wp_footer', 'add_select2_depends_js_to_footer_example' );

Also see:

Select - https://gist.github.com/ipokkel/2dab7759c694e71d7a2549bf8207dce0

Select Multiple - https://gist.github.com/ipokkel/eae1e3743b0a15b4053ff25f6757fc79