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.