There are two potential issues:
i) The carcinogenic properties of the rubber crumb. This can be overcome by a few different options. Sealing the pellets with a sealant that stops the potentially (and they are only potentially in the right combination of circumstances) dangerous chemicals escaping. The other is using a cork crumb rather than a rubber crumb. Both obviously come at a greater cost than the standard rubber crumb, but what price the possible future health of players?
ii) Infection of players with wounds. The artificial surfaces are sterile when they go down. However, as any sterile surface does, it will attract bacteria. Unlike grass pitches, there are no living beings in the ground or on the surface that will counter those bacteria so they breed and hence if a player gets a cut on the pitch, it has more chance of picking up an infection. It's not normally anything that needs more than a few antibiotics, but it is a possibility. Again it is reasonably easily solved by a regular spraying of disinfectant on the surface, but again that does cost money.
I suspect clubs are not made aware of these risks when the pitches are installed, but groundsmen are being educated by their various bodies and should therefore be communicating to their clubs the risks and the options.