AtlasDrawer
I genuinely sympathise with your anxiety. BA will do their utmost to ensure you are able to work completely unmolested should you so desire. However they cannot guarantee your anonymity.
Rest assured there will be very, very many CC in exactly the same situation, and with exactly the same worries. Many, many flights will operate, of that I feel certain. All I can say is this: Those who simply fail to turn up for a duty, or even openly declare themselves to be on strike by attending a picket line, are unlikely to be employed by BA for long, for exactly the reasons you have alluded to! This is a safety critical environment in which we work, and any 'animosity' is simply not acceptable!
When it comes down to it though, I'm afraid you just have to follow your heart and stand up for what you believe in. It's the only way to respect yourself.
Good luck to you. There will be many of us looking out for your welfare.