Foreign carriers will not fly into an airport with missiles flying around it. I'm sure already today crews aren't allowed to overnight in Israel and one or two more hits on TA all foreign flights will stop immediately.
Israel will keep it open regardless of who foreign airlines. So yes there might be some cancellations but unless they score a direct hit the airport will act like business as usual
Right after the siren sounded in tel aviv the IDF issued a statement to continue life as normal.........