Hi,
I see that you're using bootstrap and in that case, the buttons style is also done with bootstrap.
Edit the file "login" of the view "checkout" via the menu Display>Views and change 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 );
and the switcher will then use the standard radio list of Joomla instead of the bootstrap radio list.
That might help although it's less nice.