Studying tarot is quite safe for everything but possibly your wallet, once you start looking at all the gorgeous decks.
Yes! This!
Seriously though, I have had some people tell me how the Tarot is "evil", it all comes from "Satan", etc. The Majority of these people have been involved in (usually) pretty fundamentalist Christian religions. Many main-stream religions or fundamentalist off-shoots ("fundies" as I like to call them) drill into their follower's heads that Tarot and all things "Occult" are evil and are to be feared and hated.
The only real such tool that I would agree was in any degree "dangerous" is the Ouija board. As another person indicated, it opens doorways that one may not be aware of ... at least in the experience of many people.
I've been studying and using the Tarot for many years and the only backlash I've had from it is headaches if I over do it. For example, if I have several people request readings over a period of a couple of hours, or if I go to a party and do a lot of readings. Although, since there is usually so much positive energy at the parties I've been to, I usually recover fairly quickly.
So, study, learn and use the Tarot to your Spirit's content. Open yourself to new ideas and move forward. When someone tells you how dangerous Tarot is, or how you're doing the "Devil's work", smile and tell them you're sorry they feel that way and forget them. Alternatively, tell them to take a long walk off a short pier.