In the Netherlands the VNC (also a cabin crew union) has protested against the services provided by ArkeFly and Transavia to BA. They feel that no other airlines should help BA break the strike. This in anticipation of a strike at AF where they hope to prevent KLM taking over flights.
All in all this strike becomes less and less damaging for the reputation of BA. IB, LH have gone before them, AA and AF will go after them and no doubt more will follow as the aviation industry has to cleanse itself from a long history of being publicly owned.
Former national carriers have a different cost base than more modern airlines. All (not just BA) of these airlines will have to go through painful changes. I don't think BA will be anymore hurt (commercially) than AF or LH. The crew and the unions of all these airlines will have a hard time accepting these changes but without it these carriers cannot survive.