Using an if statement in the theme customizer page

Your description makes it sound like you need a radio button. Radio buttons by design are exclusive– only one button per button set can be checked at any one time.

The Settings API supports radio boxes, though the documentation for using them is sparse. I had to dig around a bit, and experiment. The key is the second parameter of add_control. You need to pass 'type' =>radio’and provide achoices` array for the radio button values.

function radio_controls_wpse_117203($wpc) {

  $wpc->add_setting(
    'radio_control_wpse_117203',
    array(
      'default' => 'hi',
    )
  );

  $wpc->add_section(
    'radio_section_wpse_117203',
    array(
      'title' => 'Radio WPSE 117203',
      'description' => 'A holder for our radio buttons.',
    )
  );

  $wpc->add_control(
    'radio_control_wpse_117203',
    array(
      'type' => 'radio',
      'label' => 'Salutation',
      'section' => 'radio_section_wpse_117203',
      'choices' => array(
        'hi' => 'Hi',
        'howdy' => 'Howdy',
      ),
    )
  );

}
add_action('customize_register','radio_controls_wpse_117203');