JSFiddle - React, Tailwind, and code Playground

HTML

Реализация на checkbox<div id="test">
    <input type='checkbox'/> 1<br/>
    <input type='checkbox'/> 2<br/>
    <input type='checkbox'/> 3<br/>
    <input type='checkbox'/> 4<br/>
</div>
Реализация на radiobutton 
<div id="test2">
    <input type='radio' name="one"/> 1<br/>
    <input type='radio' name="one"/> 2<br/>
    <input type='radio' name="one"/> 3<br/>
    <input type='radio' name="one"/> 4<br/>
</div>

JavaScript

$("#test").children('input[type=checkbox]').change(function(){
    if($("#test").children('input[type=checkbox]:checked').length >= 1){
        $("#test").children('input[type=checkbox]:not(:checked)').attr('disabled', true);
    } else{
        $("#test").children('input[type=checkbox]:disabled').attr('disabled', false);
    }
});