The report produced by the (American) Center for Health, Environment and Justice (which is almost certainly behind what you've read) correctly identified the presence of potentially carcinogenic gases in the smell which is given off by PVC shower curtains. This is hardly surprising, because the chemical composition of the gases has been known for a long time. What the CHEJ has not shown is whether those gases are present in sufficient quantities to be of any real concern.
Here's an analogy:
It's well-known that certain cooking techniques can produce carcinogens within certain types of food. In particular, cooking bacon until it's crisp (especially under a grill) increases the presence of potentially carcinogenic proteins. However, nobody has yet found any direct correlation between the consumption of crisp bacon and the incidence of cancer. Similarly, nobody has yet shown that there's any correlation between the use of PVC shower curtains and the incidence of cancer.
Most meat-eaters continue to eat bacon (often grilled until it's crisp) even if they're aware of the theoretical risks to their health. A few might choose not to do so. Similarly, most people will probably choose to continue using PVC shower curtains, but the 'super cautious' will decide to switch to alternatives.
If you never consume alcohol, always eat your '5 a day' fruit & veg, plus your '3 a week' oily fish and hardly ever touch dairy products (except possibly skimmed milk), avoid getting a sun tan and follow every other bit of health advice that's given out, it would make sense to ditch your PVC shower curtain (because it's consistent with your goal of seeking immortality). However, if you follow a more 'normal' lifestyle, the added risk (if any actually exists) of using a PVC shower curtain is so insignificant that it can probably be ignored.
Chris