Airlines are continually updated on credible threats by various agencies who can order them to stop operating but more usually arrive at a consensus view. Every airline has a security department that runs 24/7 and is headed by a vetted, experienced and highly competent individual, often ex Forces. If they aren’t, they don’t get approved.
Threat Levels are very dynamic and basically focus on intent and capability. Someone, somewhere spotted a spike in risk and cool heads prevailed.
Virtually every aspect of life is subject to the same protocols and reaction also has to be weighed against the effect any counter action may have. Partly this is down to not wanting to hand the baddies the victory of causing fear and disruption without them actually doing something overt but there’s also the practicality aspect; shutting down say the Underground is a lot more disruptive than cancelling flights to a specific destination.
Cancelling flights to say New York would be viewed differently again, each case is viewed separately and things like security measures in place / efficacy thereof also come into it.
Crews are briefed annually and tested but also get regular updates on a need to know basis. Airspace bans and choice of diversion airfield en route etc are common. We rarely get told why but comply a) because we don’t get the choice, b) because we don’t like being targets either and c) most importantly we have faith in how the system works and in those running it.