JSFiddle - React, Tailwind, and code Playground

HTML

<p class="form-row form-row-wide validate-required" id="billing_piegadatajs_field">
    <label for="billing_piegadatajs" class="">Piegādes veids <abbr class="required" title="vajadzīgs">*</abbr>
    </label>
    <br>
    <input type="radio" name="billing_piegadatajs" value="Pasta Stacija" class="radio" style="width:10%" checked="checked"><span for="billing_piegadatajs">Pasta Stacija</span>
    <br>
    <input type="radio" name="billing_piegadatajs" value="Post24" class="radio" style="width:10%"><span for="billing_piegadatajs">Post 24</span>
    <br>
    <input type="radio" name="billing_piegadatajs" value="Kurjerdienests" class="radio" style="width:10%"><span for="billing_piegadatajs">Kurjerdienests</span>
    <br>
    <input type="radio" name="billing_piegadatajs" value="Saņemt uz vietas" class="radio" style="width:10%"><span for="billing_piegadatajs">Saņemt uz vietas ( Saldū )</span>

</p>
<br>
<tr class="shipping">
    <th>Piegādes izmaksas</th>
    <td>
        <ul id="shipping_method">
            <li>
                <input type="radio" name="shipping_method[0]" data-index="0" id="shipping_method_0_flat_rate" value="flat_rate" checked="checked" class="shipping_method">
                <label for="shipping_method_0_flat_rate">Pasta Stacijas: <span class="amount">€&nbsp;3.50</span>
                </label>
            </li>
            <li>
                <input type="radio" name="shipping_method[0]" data-index="0" id="shipping_method_0_international_delivery" value="international_delivery" class="shipping_method">
                <label for="shipping_method_0_international_delivery">Post 24: <span class="amount">€&nbsp;3.50</span>
                </label>
            </li>
            <li>
                <input type="radio" name="shipping_method[0]" data-index="0" id="shipping_method_0_apg_shipping" value="apg_shipping" class="shipping_method">
                <label for="shipping_method_0_apg_shipping">DLW Kurjeris: <span...

JavaScript

jQuery(document).ready(function () {
    jQuery('#billing_piegadatajs_field')
    jQuery('#billing_piegadatajs_field').find('input[name="billing_piegadatajs"]').each(function () {
        jQuery(this).prop('checked', false);
    });
    
      // Track the click on the first set of radio
    jQuery('.radio').on('click',function(){
       
        // Get the element index , which one we click on
        var indx = jQuery(this).index('.radio');
        
        // Trigger a click on the same index in the second radio set
        
        jQuery('.shipping_method')[indx].click();
    })
});