From the article:
Erickson admits it is too early to know with certainty how serious the long-term impact could be on health, but warns that hormone-disrupting chemicals may lurk in cosmetics which could lower immunity to disease and cause neurological and reproductive damage.
I use as few cosmetics as I feel I can get away with and still look good.
As far as gender differences in cancer rates go though, even if men are not using makeup as women do, most still use shampoos, conditioners, toothpastes, soaps, colognes, deodorants, hair dyes, lotions and other skin care products which could easily contain ingredients similar to those found in women's cosmetics.
And there could be problems other than cancer from long term use of these products. Who knows? As with food, I read labels and do my best to avoid certain additives, because really, we don't know if they can cause harm later.