There are several types of easily available alcohols
--Ethanol (aka -grain alcohol, Everclear),
--Denatured ethanol (ethanol mixed with methanol, etc. so you can't drink it),
--Methanol (aka -wood alcohol and HEET-yellow bottle),
--Isopropyl alcohol (aka -rubbing alcohol)
They are all toxic.
OSHA publishes the recommended PEL (Permissible Exposure Limits) for various substances. Ethanol is 1000 ppm, isopropyl alcohol is 400 ppm, methanol only 200 ppm, and in denatured alcohol they often add a percent or two of methyl isobutyl ketone which is only 100 ppm. The lower the number the less safe (more poisonous) the substance is.
So pure ethanol is the least toxic of this group. It is expensive due to liquor taxes, etc and hard to get in some states.
That said, the others have been safely used by tens of thousands of campers and boater for decades (probably centuries). Avoiding prolonged skin and vapor exposure, using it outside in well ventilated areas, and keeping them out of your eyes and mouth is the key.
I would bet that it is much more likely that you will get burned by your stove than suffer a toxic exposure.