The default is to have no fx:id attribute at all. I just tested by adding a single button to a new document and saving.. this is the result:

<?xml version="1.0" encoding="UTF-8"?>

<?import java.lang.*?>
<?import javafx.scene.control.*?>
<?import javafx.scene.layout.*?>

<AnchorPane maxHeight="-Infinity" maxWidth="-Infinity" minHeight="-Infinity" minWidth="-Infinity" prefHeight="400.0" prefWidth="600.0" xmlns="http://javafx.com/javafx/8" xmlns:fx="http://javafx.com/fxml/1">
<children><Button layoutX="231.33837890625" layoutY="38.0" mnemonicParsing="false" text="Button" />
</children></AnchorPane>

But as soon as you enter anything in the fx:id field then you get the fx:id attribute and you can't get rid of it..even by hitting the little button at the side of the edit box and selecting "Reset to default".
<?xml version="1.0" encoding="UTF-8"?>

<?import java.lang.*?>
<?import javafx.scene.control.*?>
<?import javafx.scene.layout.*?>

<AnchorPane fx:id="" maxHeight="-Infinity" maxWidth="-Infinity" minHeight="-Infinity" minWidth="-Infinity" prefHeight="400.0" prefWidth="600.0" xmlns="http://javafx.com/javafx/8" xmlns:fx="http://javafx.com/fxml/1">
<children><Button layoutX="231.33837890625" layoutY="38.0" mnemonicParsing="false" text="Button" />
</children></AnchorPane>


With Scene Builder 1.1 the results is different. We start with:
<?xml version="1.0" encoding="UTF-8"?>

<?import java.lang.*?>
<?import java.util.*?>
<?import javafx.scene.control.*?>
<?import javafx.scene.layout.*?>
<?import javafx.scene.paint.*?>

<AnchorPane id="AnchorPane" maxHeight="-Infinity" maxWidth="-Infinity" minHeight="-Infinity" minWidth="-Infinity" prefHeight="400.0" prefWidth="600.0" xmlns:fx="http://javafx.com/fxml/1" xmlns="http://javafx.com/javafx/2.2">
  <children>
    <Button layoutX="256.0" layoutY="102.0" mnemonicParsing="false" text="Button" />
  </children>
</AnchorPane>

and if you edit the field and then clear it you get the same thing.. no fx:id attribute at all.

NetBeans is expecting to see a valid string for the fx:id and will generate code in the controller (via the Make Controller action) using whatever string it finds. So it generates a line of code that looks like this:

@FXML
AnchorPane ;

with no identifier.

I have also filed this as NB bug #240005