Hi,
Yes, I know you're using the bootstrap design feature.
And that's why I said that you should try to turn it off and see if that helps because the problem is probably that your Joomla template doesn't properly support bootstrap and must be missing some bits for the radio labels.
Well, a solution is to turn off bootstrap for the switcher element by changing the line:
echo JHTML::_('hikaselect.radiolist', $values, 'data[register][registration_method]', ' onchange="displayRegistration(this)"', 'value', 'text', $defaultSelection, false, false, true );
to:
echo JHTML::_('select.radiolist', $values, 'data[register][registration_method]', ' onchange="displayRegistration(this)"', 'value', 'text', $defaultSelection, false, false, true );
in the file "login" of the view "checkout" for your frontend template via the menu Display>Views.