Political symbols at work

A photo that appeared to show an NHS healthcare worker wearing a Palestine badge caused a heated debate on social media. Some say during the current conflict between Israel and Hamas, the Palestine flag becomes a political symbol and therefore breaches the principal that NHS staff should appear to be impartial. Others point to a double standard and question why the poppy can be worn by state sector workers even though some believe it is a political symbol. What counts as 'political' and how free should we feel in the workplace to express our beliefs?