According to 'elf and safety, exposure to the dust may cause severe eye irritation, and skin may experience redness, swelling and blistering if exposed to the dust for an extended period. Polyurethane resin dust also poses danger when inhaled, and can irritate the respiratory tract or contribute to rhinitis and asthma.
Which sounds really bad, except that even building a resin kit your exposure is minimal, and you can follow the advice already given to reduce it even further.
As regards inhalation of the dust, the horror stories are based on experiments with rats, carried out in the 1970s. The poor old rats were exposed to particles of polyurethane resin via intratracheal intubation. That means that the dust was effectively blown into their lungs. Unsurprisingly this had various adverse effects. Again, it is easy to mitigate any chance of inhaling the dust by following the advice already given in other answers. The biggest problem I have with the dust is that it clogs my files!
You should not let the supposed and often exaggerated hazards of working with polyurethane resins put you off. I find it easy enough to work with safely and there is no reason why anyone else should not be able to do the same.