There have been suggestions that inhaling talc might possibly lead to an increased risk of lung cancer but there seems to be little scientific evidence to support the theory. (Even those studies which suggest that there might be a link only relate to massively high exposure levels, such as among miners who dig the stuff out of the ground; there has never been any suggestion that, for example, inhaling a few particles of talc from the air in your bathroom can have any adverse effects)
There have also be suggestions that the use of talcum powder in the genital area might very slightly increase the risk of ovarian cancer in post-menopausal women but scientific studies have been inconclusive.
There has never been any suggestion that ingesting small amounts of talc into your stomach can cause harm and the World Health Organization only classifies talc as carcinogenic if it contains asbestos fibres (which modern forms of talc don't).
I'm frequently amazed that some people seek to avoid alleged carcinogens (which are actually completely harmless) while often happily continuing to consume those classified as 'high-risk' carcinogens by the World Health Organization, such as tobacco, alcohol and processed meats (e.g. ham, bacon and sausages).