Alum blocks and their slimmed down form, styptic pencils, have a long history in traditional shaving. The blocks are used after a shave, rubbed over the entire face and the pencils are used as an astringent to prevent bleeding from small nicks and cuts. Alum is crystallised hydrated potassium aluminium sulphate, also the ammonium and sodium salts are very similar, and what causes the doubts about it is the presence of the metal, aluminium.
When I was young a lot of the pots and pans in the kitchen were aluminium, it is perfect for the job because it is light and conducts heat well, yet now you never see aluminium used in cooking. This is because it is toxic to our nervous system and bone structure. In addition Wikipedia says that the use of aluminium in antiperspirants is “controversial” as it is a possible factor in breast cancer and in Alzheimer’s disease, with brain plaques of sufferers showing an elevated presence of the metal. There is an article about aluminium toxicity here.
Although the use of alum in shaving is external, human skin is not impermeable and the action of shaving causes many small cuts and abrasions that do not bleed but which would ease the absorption of aluminium into our bodies. And of course styptic pencils are used directly on bleeding cuts, which must transfer some of the chemical into our systems.
There are alternatives to using alum for cuts. As I wrote in an earlier article about bleeding and shaving, a thorough splashing with cold water will stop most small nicks and weepers, the cold constricts the capillaries supplying blood to the surface of the skin. Anything still bleeding after this can be stopped by putting a small piece of paper tissue on it, this enhances the natural clotting mechanism by vastly increasing the surface area that it is working in and the tissue can then be removed after a few minutes.
Of course it is up to you, if there were a medically proven danger then alum would already be banned for human external use. However medical knowledge is very far from perfect and often lags a long way behind what is actually happening in the world. You choose.