Yes, on this basis she probably has a good case, particularly now that Palestine has been recognised by the UK as a sovereign state.
“I was informed that while rainbow lanyards and other historically permitted symbols such as the Ukraine flag were fine, a Palestine pin was unacceptable,” she explains on her Crowdjustice page, set up to help fund her legal fees.
As
@Ilovemusic says, the NHS should never have become a place where staff are openly permitted to signal their personal beliefs. When I worked for them, everybody wore the standard blue NHS lanyard and people wearing ideological badges would have been asked to remove them for being unprofessional.