I managed to get it working like this:

    $form['color_select'] = [
	  '#type' => 'radios',
	  '#title' => $this->t('Pick a color'),
	  '#options' => [
	    'blue' => $this->t('Blue'),
		'white' => $this->t('White'),
		'black' => $this->t('Black'),
		// 'other' => $this->t('Other'),
	  ],
	  '#attributes' => [
	    'id' => 'color_select',
		'name' => 'color_select',
	  ],
	  '#states' => [
	    'checked' => [
		  ':input[name="color_select"]' => [
		    ['value' => 'blue'],
			'or',
			['value' => 'white'],
			'or',
			['value' => 'black'],
		  ],
		],
      ],
	];

Although I'm not sure how it works now. Does it actually set the radio button on checked when the value is one of the given value ones?