Let me clear up a thing or two. Even as militant as those small Cuban protestors & their polititians may be, the police would never allow them just to go & protest on the runways of MIA, no way, Jose
. Most Cubans in fact are opposed to these demonstrations. FLL (Ft Lauderdale) will be fine, so if you fly there, there should be no problems. There has been a protest in West Palm Beach, but not in the airport. Don't expect anything there, either.
Now, as for Miami International Airport, I have been told by my very good Cuban friend, (who was completely right about where the first demonstrations took place, i.e the port, just like I informed you) that MIA will be affected this Monday, JANUARY 10, by a protest. He doesn't know exactly at what time or what this will involve, but I think it will be a slowdown or blockeage of traffic to & from the airport. They might drive very slowly, 5 mph, through the airport, or block the access & or the connecting streets, for a few minutes, although it could last for half an hour. So this Monday, don't worry if you are caught in this, or if your ride is late, they'll get there eventually, just a little late. There won't be a massive shutdown or nothing like that. That's it. Just relax & don't change your plans.