Interestingly (for me), this is a subject I've read about quite recently.
There was a class action law suit in the USA in which a number of women (or their families) received record damages on the basis that Johnson & Johnson talc caused ovarian cancer. Likewise, there have been two or three individual cases where people have been awarded damages because of talc use and ovarian cancer. The argument goes that talc used by women on their sensitive parts can theoretically travel internally via the fallopian tubes to the ovaries and might cause inflammation, which in turn might lead to ovarian cancer.
The key word is "might", although clinical studies mainly find no causal link.
Another link between talc and cancer comes from the fact that when mined from the earth, talcum powder contains asbestos. However, refined talc has been asbestos free since the 1970s.
The connection to lung cancer is associated with the workers who mined talc - because they were exposed to the asbestos contained within the unrefined talc. Clinical studies into a causal link are mixed. But, studies show no medical correlation between talc use and lung cancer.
The International Agency for Research on Cancer (part of the World Health Organisation) added talc to its list of known or possible carcinogens. However talc is categorised under Group 2B, which are things identified as being "possibly carcinogenic to humans".
The emphasis is very much on the word "possibly". Basically, they might cause cancer, but we don't really know. Coffee is on the Group 2B list.
So, I'd be very wary of stating that talc is carcinogenic.
It can certainly be an irritant, can make the dance floor dangerous, and can ruin your camera. And people who say that they only put a little bit down in the corner (or wherever) fail to appreciate that it spreads - it spreads via the soles of your shoes, on clothing, and through the air. It gets everywhere!
And I've yet to see anyone using talc do little more than Dad (or Mum) dance.