Before we all pile up further on Ditto, his advice to bring a printout attesting your rights to travel is good advice.

Especially if you have some non standard documentations, beacuse we all remember those legit UK residents who were EU citizens who were denied boarding because there is no printed doc and the rest of the world wasn't yet aware.

As others have said, and rightfully so, it is NOT the passengers burden to have to prove their right, but if you can, it certainly cannot hurt.