the thing is we can't base strikes on 'what the press and public will think of it'. The press will demonise every strike, except occasionally FBU cos its hard to sell 'look at these bastards wanting a decent wage! for going and saving people from burning death!'
no matter how righteous your reasons for the workplace dispute, you will be crucified in the press. So why give a fuck what they say? If individual customers are out of pocket, tell them why.
A strike won't even garner the support of the 'labour' party. They like union money but they don't like backing union disputes.
so inevitably it comes down to defending the pay and conditions you signed up for in good faith.