Recording is absolutely allowed in airports, even in some (thought not all) TSA and CBP secured areas. The First Amendment audit folks went nuts (in a good way) a few years ago when this video was posted, because an officer actually knew the Constitution and applicable law and refused to halt filming in an airport. Now, not every LEO and airport employee knows the law, but this gentleman clearly did and protected the filmers' right to record. https://www.youtube.com/watch?v=G1CjZN2H5-8https://www.youtube.com/watch?v=m5ZiMoo43HU
Now, semi-public and private places are subject to different rules, as I stated earlier. And yes, airlines can attempt to prohibit photography of their personnel and can write such things into the CoCs and other policies. However, if the photography is being done in a public or in certain situations semi-public locations, then the First Amendment will trump those internal airline rules.
It all comes down, in the end, to an expectation of privacy. Many would argue that there is no such expectation in a crowded airport terminal, especially if you're an airline worker manning a busy customer service or gate desk where your job entails interacting with large swaths of the public. Think about it - how would the news media be able to report on airline and airport issues if they couldn't film within a terminal at times for fear of taping a random airport or airline worker? They wouldn't be able to, which would chill free speech. But, since there is no reasonable expectation of privacy in a crowded airport terminal, they can.