JSFiddle - React, Tailwind, and code Playground

HTML

<form>
<label>Start date: <input type=date id="start" required></label>
<label>End date: <input type=date id="end" required></label>
<input type=submit>
</form>

CSS

label {
    display: block;
}

JavaScript

var start = document.getElementById('start');
var end = document.getElementById('end');

start.addEventListener('change', function() {
    if (start.value)
        end.min = start.value;
}, false);
end.addEventLiseter('change', function() {
    if (end.value)
        start.max = end.value;
}, false);