As I had the same issue I looked at the code and it seems as this is easy to fix. It boils down to removing the validation for the “radio” field like this:

remove_filter( 'wpcf7_validate_radio', 'wpcf7_checkbox_validation_filter', 10 );

Be aware that this globally disables validation for “radio”. I don’t see any side-effects right now but be aware what you are doing here.

For anyone wanting to dig deeper, this is the relevant change in 4.9: https://plugins.trac.wordpress.org/browser/contact-form-7/tags/4.9/modules/checkbox.php#L206

• This reply was modified 6 years, 6 months ago by Thomas Kräftner.

Here is another solution if you still require some radio buttons to be required:

Add a required class to your radio fields that still need to be required:

[radio theName class:required "Yes" "No"]

Then add this code to functions.php

remove_filter('wpcf7_validate_radio', 'wpcf7_checkbox_validation_filter', 10);

add_filter('wpcf7_validate_radio', function($result, $tag) {
  if (in_array('class:required', $tag->options)) {
    $result = wpcf7_checkbox_validation_filter($result, $tag);
  }
  return $result;
}, 10, 2);