If I understand correctly your field has 2 options
1) red
2) blue
If you update the field with the value checked, to which value should it apply ?
You haven’t provided a real value which should be stored, only a string which does not occur in your options.
And… checked is only used by checkboxes (afaik).
In this case you would have to actually set the value of what you want to save.
So you would have to save red or blue (assuming those are both the id and value).
So I think you would have to do something along the line of:
update_field('field_1234567890', 'red' );
update_field('field_1234567890', 'blue' );
