The big “toxic trio” nail polish are dibutyl phthalate, toluene, and formaldehyde. Those are real toxins, the kind without scare quotes.
Of course, for a single application of nail polish exposure we’re talking about really small amounts. There are brands that don’t use these chemicals, but the average person isn’t likely to either read the microscopic print on the teeny bottles or research the matter. Some people are more sensitive than usual to the chemicals, and certainly the risk of exposure is greatest for nail salon personnel.
But don’t poo-poo the notion that potential hazards aren’t included in make-up.
I already mentioned the lead acetate in Grecian Formula. While many hair dye ingredients that used to be common have been removed from modern formulations due to known hazards, there are still thousands of ingredients used these days, it’s likely some of them are less than healthy for you. Read the cautions on the boxes - hair dye, as well as several other hair treatments, can cause eye damage if improperly used. Not so much a toxin but definitely a potential hazard.
When it comes to lipstick, there are ingredients like methylparaben which are banned in Europe but common in the US. Which, by the way, it a common theme when you look into these things, chemicals allowed in the US but banned elsewhere. Propylparaben can cause skin reactions in the amounts used in lipstick in particularly sensitive or allergic individuals. Again, there have been various coloring agents/dyes that used to be used that are now banned, which means today’s lipsticks may be safer than those of prior generations, but that doesn’t mean everything is perfectly safe.
Rinse and repeat for every type of make-up you can conceive of - foundation, blush, eyeliner, eye shadow, concealer, etc.
Again, a lot of the effect is in the dose. Women who wear cosmetics only sometimes are most likely at negligible risk. The human body does have mechanisms to deal with chemical hazards and we’re exposed to them through air, water, food, and everything else we come into contact with every day. Women who are heavily made up every day, though, are getting exposed to these ingredients more often, and at least some will suffer negative effects. And some of us are too sensitive to wear this stuff even occasionally without consequences.