Safe? Relative concept to me. They are higher risk than lead-acid, so I think they need some extra care. Original cubs are less likely to catch fire post-crash than most other aircraft, because they don't have an electrical system at all. But we've traded the inherent risk of having an electrical system to get things like starters and radios. The same could be said for gasoline. In the air, certified aircraft are pretty good with fuel safety. But in a crash, not so much. There are similar issues. The in-flight charging risk is addressable. Trickier to handle impact resistance, but it's not impossible, and we already have that risk with lead-acid. The fire risk on impact is from the ignition of the fuel, not the battery itself, just in terms of area of coverage and energy level.
Actually I think the real danger for li-po's is in transport category aircraft. Boeing is or was using them in 787, in the 50lb range. Maybe they have them setup so if they catch fire, they'll burn their way out of the aircraft and fall before they cause the aircraft to fail. I don't think it's possible to design a safe container that weighs less than NiMH/NICd and would prevent causing external damage, but I could be wrong. I'm certain it isn't possible to design a battery pack incapable of failure. But maybe it's an acceptable risk.
Yep, speaking of LiPo. That's where I have my experience. No idea how the risks translate, but suspect they're closer than the manufacturer would like people to believe. Lithium is used in batteries because it's light and high energy. That reactivity is what makes it dangerous.