matblack, a very good question.
Simple answer is yes.
Poor industrial relations do affect flight safety. People (even highly-qualified professionals) can get distracted. When they get into work to check in for a flight, they can find the latest bulleting from either the company or the union in their internal mail, and can get annoyed or distracted by that.
Relations between pilots can become more difficult during a period of industrial unrest. Some can get very heated indeed. The BEA Trident that crashed into Staines reservoir is a case in point. That day in the crewroom, his FO had been a witness to his captain's tirade against "anti-company" pilots.
As Blue Eagle says, the pilots are just as anxious to get home safely as you are, but they can get distracted and stressed by such matters.