We'll basically I have whmcs version 5 and normally in the general settings of the setup menu in the admin side of whmcs, you should come across the "Default Order Form Templates" from the Ordering tab. There are at-least 8 different order form templates: ajaxcart; boxes; cart; comparison; modern; slider; verticalsteps and web20cart.
Upon testing all the templates only the "cart" order form template works perfectly with the whmcs bridge plugin. Web20cart works ok however in the checkout the login form or the sign up with "your details", doesn't show up.
The other templates when ordering domains it doesn't load correctly.