I can confirm that it is possible to do custom form validation on Squarespace forms, even after their switch to React. I can't post the solution we're using, but we are able to block form submission until custom validation rules are satisfied.
Just attach an onclick event to the form submit button, when clicked if the custom validation rules fail then use javascript to cancel the click event. With jQuery cancelling the submit button click event is something like this:
evt.preventDefault();
evt.stopPropagation();
evt.stopImmediatePropagation();
return false;