To stay is to explicitly condone the actions of the leadership.
By "to explicitly condone" you seem to mean to implicitly condone.
inject itself and its considerable demographic and monetary clout directly and voluminously into any political debate that takes its fancy. Many european states, learning from experience, outrightly ban such behavior
That's a strong accusation. What specifically is banned by whom?
Your main point is wrong, BTW. If the label is important to people, they should be reluctant to drop it. They can't do anything about the people who are giving it a bad name at the moment, and it's unreasonable to expect otherwise.
"The battle for the world is the battle for definitions" - Thomas Szasz