JavaFX: Removing child from a Group causes Exception

Free

You can't directly modify a List while you're iterating though it. The iterator gets confused.
Do

List<Node> nodesToRemove = new ArrayList<>();
for(Node node : g.getChildren()){
    if(node instanceof Text){
        nodesToRemove.add(node);
    }
}

g.getChildren().removeAll(nodesToRemove);

or (I think):

for (Iterator<Node> iterator = g.getChildren().iterator(); iterator.hasNext();) {
    if (iterator.next() instanceof Text) {
        iterator.remove();
    }
}

or, in Java8,

g.getChildren().removeAll( g.getChildren().stream()
    .filter(node -> node instanceof Text)
    .collect(Collectors.toList()));