If you're editing an Entry, change the text, and then hit the "Save" button, the first event that fires now is onBlur (see here for more context).
The onBlur results in a save being triggered, and this.state.editing is unset. After that, the save button onPress is now triggered (previously this came first).
To avoid the onPress causing us to go back into an editing mode, we can ignore it here while the save is ongoing.