Do you pump your own gas? Chances are you are exposed to more benzene and other carcinogens doing that than you are from hand sanitizer.
With that said, I use hand sanitizer very sparingly because it's just not necessary. If you wash your hands with soap, that is more than sufficient. And it's absolutely unnecessary and overkill to wash your hands and then immediately use hand sanitizer.
I would avoid the brands specifically called out in that story, but overall, this is not something that you should be overly concerned or lose sleep over. And if a hand sanitizer is petrochemical-derived (as opposed to an alcohol made via fermentation), not entirely surprising.
Edit: I saw you've been using one of the brands for a year. I still wouldn't be concerned, mainly because there is nothing you can do about it.
Remember, the dose makes the poison. Typically, the limits for contaminants like that are set WELL below the amount that can actually do any harm. So, even if you used one of the brands with the highest amounts, you weren't likely to be exposed to enough of it to cause cancer.