First, I hope everyone understands that this underwear thing is a little overblown, and to some extent a Union ploy to attempt to manipulate public sympathy into assisting them in their negotiations. The number of cast members affected by this issue is probably in double digits, and when you consider the 12,000 cast members that the Service Trades Council represents. I understand that it is a pretty negative situation, but it has been addressed and resolved.
On the strike front, whether there is a "no strike" clause or not, the union has threatened strikes, and sick-outs in the past. During my many years with the company I have seen several instances where managers and office workers were being quickly trained on various locations in the event of a strike. That being said however, you need not worry about a strike. The union will never call for one. Florida is a "right to work state". If cast members walk out the Company has a right to go ahead and fire them and fill their positions. Most cast members can not afford to lose their jobs, so most would not walk-out. Also, I have seen many instances where the Union threatened strike if certain demands were not met, the Company said no, and the Union immediately went back to its members and said the contract was great and that membership should approve it. After the last round of negotiations, membership dropped significantly because the Union really failed to get any concessions that they had said they would get going in, yet still said they had negotiated the best they could get. The Union will never authorize a strike, your vacation is safe.