I will say safer than gasoline, but different, needs a good deal of self-educating before handling, but to be honest, I doubt that all the cell phones around the world with the same battery tech (albeit smaller, but when else do you have a LiPo pack next to your ear?) have done anyone any reasonable harm from batteries cooking off.
I was really scared after watching the videos on youbube, and only considered LiPo when I realized how much I was paying for a single 28V Dewalt pack and all the trouble I was going to to get them to work, and how much more cost effective LiPo was, then when I heard about the new nano tech turnigys, I took the plunge!
I can't speak from anything but a wet behind the ears novice with a good dose of cation and using high quality proven charger, and I balance my cells every charge. I am only 5 charge cycles through my 6 packs, but I can say that by following the expert advice here on ES, that not ONLY have I not damaged a pack or even a single cell in a pack, but I have not even had the packs, wires, ESC or motor even heat up under 118A draw (momentarily burst, constant more like 60A)!!!
I had a LiPo pack that had puffed up but still charged and discharged normally given to me by my local hobby shop, and did some torture testing of my own. This pack wasn't over charged, but just had a nominal charge and I set about shooting it with my high powered .22 pellet rifle (same power as a .22 short).
I then dropped it in a bucket of water. NO reaction, no nothing! I was really disappointed! :lol: I was expecting a firework show. Mind you I was blowing holes ALL THE WAY THROUGH this 4s 3000 mah pack, not just denting it. I even put holes through the puffed up cell and it didn't let out so much as a "pop".
I'm still planning on putting either a metal or high temp plastic case on my 4s 6000 x3p (15v 18ah pack) but for now I have a LiPo charging bag for extra insurance, and no problems or worries so far.
I think you have a MUCH greater chance of problems with a motorcycle or gas bike, I'll never forget the race where some guy's fancy schmancy synthetic oil started leaking from the heads of his FZR Race bike spraying his leathers on the legs and starting to burn, and here his is just riding normally while all the corner workers are trying to flag him down!!!
You NEVER saw someone do the "ants in my pants" dance on a bike going 60 - 80 MPH so comically!! (His leathers protected him, no injury but man it was scary and funny!!!
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Buy a good quality proven charger with a good track record, use a pyrex (corning wear) cooking pan or LiPo charging bag and DO NOT LEAVE while charging, have an exit strategy if they were to catch fire (very rare if you follow the previous) so you can get them out of the garage fast.
Don't charge them in the living room, do it somewhere it can take some heat or if you don't mind taking the chance of losing $300+ of good charger & power supply, charge in a BBQ pit or other such place outside and let 'em rip.
I also think a big part of this is being really kind to them, don't do more than 80% discharge EVER, and in the first 10 cycles no more than 50% (if it's cold maybe only 30% durring the first 10 charges)
I'm no expert, but I am careful, and I paid extra for really good LiPo instead of the cheap stuff, and I haven't had ANY issues yet.