I can't see recent developments affecting skilled professionals. At the worst there may be some extra paperwork to navigate through that didn't exist before but I doubt that it will be a complex issue.
There are many Europeans who live and work for UK airlines and BA at first glance seems to employ a sizeable number of Europeans, relative to the number of Brits who are employed at other European flag carriers. I suspect BA and many other UK airlines will not be changing their recruitment policy soon.
If you want an existing example of diversity and free and open borders within the aviation industry within Europe, look no further than the UK. To think that someone from the other side of the world with the right to live and work within Europe will suddenly be more employable than someone from the UK is totally unrealistic.
I disagree. Airlines have shown themselves to care only about cost. Additional cost associated with employing similarly qualified crew should favour UK crew. Relative experience is immaterial. The current UK situation, whilst it may be an example of diversity, is also an excellent example of why freedom of movement of workers is much less valuable to the average Britain. The EU rules are not applied quite as equally as we all would hope.
The lazy argument is that the British are generally worse at languages, yet my experience is of a reasonable number of multilingual British pilots who would never have an opportunity in foreign carriers.