I sometimes do fire breathing, alongside fire spinning. Pretty much everyone who breathes fire as a hobby or performs professionally uses high purity paraffin.
Alcohol is bad because it burns hot and gets you drunk while you're doing it (very bad) and doesn't make a very impressive flame in comparison.
But yes, it's very dangerous. I refuse to teach anyone who I ever remotely believe will try to shortcut the safety procedures that are designed to make it at least not kill you most of the time.
The short list of safety stuff looks something like this:
1. Don't wear synthetic clothing, especially not nylon or polyester. That stuff will melt if it burns. You're actually better off with bare skin, but really you should wear something that doesn't burn easily.
2. Use a sturdy bottle (won't break if you drop/throw it) with a self-closing valve. If something happens, this will let you ditch the bottle fast and free your hand up for more important things. Last thing you need in an emergency is for your fuel bottle to spill fuel everywhere.
3. Have another fire breather watching you with a fire blanket for safety. If something goes wrong, it's their job to more or less tackle you and smother the flames as fast as possible. And if something really goes sideways, it's their job to call 9-1-1.
4. Check constantly for wind direction, and definitely don't try anything if the wind is unsteady.
At my daughter's school, they had that project week, too. Easily the most important experience in grade school IMO. They put the liquid inside a tube with a non-return valve. Also, all-time adult supervision, clear instructions upfront and kids did not get the tubes until they needed it. Kids were 8/9 years old. Yes, you have a significant risk and I am very glad they took it to help the kids grow up to be responsible people who can take limited risks.
If your doing both fire-eating and fire-breathing in the same act, then it's important to do them strictly in that order.
As for toxicity, you can fire breathe with pharmaceutical grade paraffin(kerosene), if you accidentally swallow some, you'll just experience its laxative effects
There is also the possibility to use cornstarch, flour or other powders for fire breathing. This should be safe, you shouldn't inhale the powder though.
I did it once, when I was around 12 years old. It looks a little less cool than with fluids, but it was still an awesome experience.