It's just about impossible for anyone to predict what's going to happen in Greece at any time. There could be strikes or other labour problems, but I suspect that's the worst you would have to face. If Greece were going to exit the E.U., this wouldn't happen overnight so it's likely things will still be "business as usual" in June and July.
Greece was also facing turbulent times when I was last there a few years ago. I found that predicted demonstrations never materialized, everything was stable with the financial situation, and I had a wonderful holiday.
Regarding Aegean Air, I've flown with them a number of times and my impression has been that they're very much a "class act" and the flights were very comfortable! I believe they're a publicly traded company, and they seem to be in expansion mode, as they recently bought-out Olympic Air (both airlines will operate under separate brands). They also picked up a number of routes when Cyprus Airways went bankrupt. It should also be noted that Aegean has won quite a number of awards including the SkyTrax Best Regional Airline in Europe award at least five times, including last year. Again, no one can predict the future, but they are definitely my preferred airline for flights in that part of Europe.