Glycerine doesn't affect everyone. As for parabens, they are in SO many other products as well. For the cancer, The long history of safe use of parabens, the fact that many occur naturally and can be consumed without adverse effects also adds reason as to why its use is so widespread. A study in 2002 specifically stated that methyl paraben is not carcinogenic or mutagenic meaning it does not cause cancer and it does not cause DNA in cells to change ( Food and Chemical Toxicology, pp 1335-1373, 2002). The study where tissue found with cancer wasn't tested against the tissue of healthy breast tissue meaning no surefire answer that parabens were the culprit. This one study does not prove a cause and effect relationship between parabens and cancer.
More on it:link
The study was small - samples were taken from only 20 women.
There were no controls - normal breast tissue was not investigated for comparison.
No other parts of the body were studied - theoretically, parabens may lurk elsewhere in the body.
The source of the parabens was not identified - no one knows if they came from antiperspirants, other personal care products, or possibly a household source.