Wordpress Contact Form 7 radio not required
A workaround would be to use a checkbox and add the exclusive parameter. This allows you to submit the form without selecting a customer type.
[checkbox customer_type exclusive "New Customer" "Old Customer"]
Checkbox exclusive actually didn't work for me because of theme's CSS which didn't support it.
Without bothering with adding JS and CSS to the theme to support this feature I have managed to overcome the problem with radio by using one more "empty" field:
[radio choice label_first default:1 "" "Yes" "No"]
After that in CSS i added:
.wpcf7-list-item.first {
display: none;
}
This selected first option which was not shown in front-end (and resulting mail) and made checkbox effectively non-required in validation.