All answers are to be found on the net through Google. You could listen for ten years to individual people (Woodworkers) on this subject and you will get as many variations as persons.This problem is not one of exotic versus grown in country of origen but the very nature of individual timbers. Scientific Studies on this subject are legion,suffice to say what affects you me and the next person depends on mitigating factors such as health ,environment and age.
An example many years ago we had demos by an American Woodturner who demonstrated around the world turning on a lathe Western Style hats. In our instance world famous and knowlegeable turners provided a 40 kg block of Silky Oak,the guy used it and broke out in extreme blisters and a terrible reaction needing urgent medical treatment. In my youth Silky Oak was readily available in Australia and used for a huge number of projects safely on buildings and furniture.
Asking this question that is as broad as it is long can be brought down simply by listings already known telling which timber to use or avoided at all costs,indeed many are carcionogenicilly defined. Easily found on the net. In my wood group we have lost a few members to allergic reactions to timber.
Good fortune in your quest.
A serious problem existed with automotive fuel petrol here in Australia causing dependance,death resulting in a huge number of indiginous people sniffing the substance. This an example of wrongful use of Petrol. Aeroplanes were drained at airports where essential services were disabled to feed what was defined as a habit resulting in the case of Outback mercy flights had to be cancelled using the Flying Doctor Services etc,results deaths of patients.
Your question needs you to do the research initially,if you feel inclined to pursue woodworking as has been said you should take basic precautions personally and in every workshop.Recently in my Wood Guild a demonstrator attempted to turn a huge block of Aussie timber of aq huge size simply forgot to check the speed of the lathe,started it up on full speed the timber flew off the lathe,smashed a window and landed on this guys head causing severe injuries. This man has been an academic and knowledgeable woodworker in retirement now so allergy matters are but one part of woodworking that demands personal research. Good luck.
Peter.