A strike almost NEVER gains public support/sympathy - esp. in the transport sector, and ESP. "fat cat" pilots.
May I suggest that one of the most effective tools that can be used to GAIN public support is ACTIVE involvement by the pilots in EXPLAINING the reasons WHY they are taking action.
Leaflets handed out, at airports, to the passengers affected, explaining how degraded rest conditions for YOU, directly impact THEIR immediate SAFETY, because of the increased RISK of DANGER, is time and money well spent.
Let them know that you - the pilot group - are on strike for the SAFETY of your passengers, whilst management are interested only in their MONEY!