If Prospect are actually saying as you quote. Then they actually need people to remind them who they serve. Believe me though, it's not just a Prospect problem...
It doesn't matter who they serve or which properly constituted union it is they have no choice. They can campaign as much as they like using legal means until it becomes law. Once it is law and a requirement they can't advocate breaking the law as to do so would leave the union and its officers open to legal redress. They also have a duty of care to their members so although they might offer support if you chose to face up and refuse to have an id card they can't suggest such action or condone it because you might subsequently decide to sue them when you're out of work and the House of Lords and European Court turn out to be unsympathetic.
The only people who think this is a good idea are a handful of senior Civil Servants and Cabinet Ministers. Unfortunately they have the majority to push it through and by the time of the next Government they will have commited so much public money to the project that the next Government of whatever colour will have little choice but to carry on as they'll need the income from issuing the cards to pay the contarctors.