Rico - as a transport provider, safety is important, but the obligations of the provider presumably stop at some stage. If a passenger wants to go somewhere, can an airline say "we know best and will not let you fly" ? Just because one section of the capital of a country is suddenly news-worthy, doesn't mean the rest of the country is as well !
If pre-booked passengers are in an area of the world which has seen recent dramatic events and want to get out, an airline presumably also has moral obligations to send the plane from their home base to get those customers to safety.
Yes - an airline has a moral obligation to ensure you're safe during passage. An airline may have a moral obligation to ask a passenger at check-in "are you sure you want to fly", but at some point the passenger has to take on some kind of responsibility for their own safety.