In surveys of public opinion, more than 80% of Australians support research into stem cells so the word "controversial" is not really accurate. Originally, controversy arose around the use of embryonic stem cells. Hardly any research in Australia now involves such cells. Most of it is on adult stem cells or their derivatives, such as induced pluripotent stem cells (iPSC). When you go to the relevant web sites, you will be able to find these things out for yourself.
The pressing ethical issue currently is the growth of private commercial clinics claiming to provide stem cell treatments for a wide range of diseases. Their treatments are largely untested in proper clinical trials, very expensive, and the companies prey on the fears of people desperate for help for their illnesses or those of relatives or friends. One might argue that there ought to be more controversy about this.