It is important to understand the difference between crystal deodorants and traditional deodorants.
Crystal deodorants are focused on bacteria and not sweat whereas antiperspirants are focused on reducing sweat and not necessarily bacteria. This makes it difficult to compare them head to head based on the same criteria.
Crystal deodorants form a mineral layer on the skin to prevent the overgrowth of odor- causing bacteria. Although the traditional aluminum chloride is not found in this product, there is a different type of aluminum compound in these. Because it can take a few days for this to change the bacterial environment under the arms, it may not be as effective initially on odor but can gain effectiveness over time by reducing bacterial overgrowth.
The only case reports out on crystal deodorants are reflective of some of the irritant reactions to the product but these same types of irritation can also be seen with traditional antiperspirants.
If you are looking for an alternative to traditional antiperspirants, this is a reasonable option to try. Although still focused primarily on odor and not reducing sweat, many do find it is effective as a deodorant.
It is always such a difficult question as to whether it is worth the hype. The answer is completely based on the patient’s perspective.
The overall answer is that it really has not been shown in epidemiological studies that breast cancer and traditional antiperspirants have a connection. This means that when you compare two populations of women with and without breast cancer that used and did not use antiperspirants there is no difference in the incidence of breast cancer.
The story behind Alzheimer's and any possible links is impossible to state with certainty as the cause of Alzheimer's is clearly a big unknown. I have even published papers with a colleague showing a possible connection between untreated Lyme disease and Alzheimer's disease- this has nothing to do with antiperspirants!
Personally I have a family history of breast cancer and I use traditional antiperspirants. I have not seen convincing data to support trying other options. I have tried the natural products and find them to be unpredictable in terms of effectiveness. Some days they work, some they don’t.
That being said, it is important to do what makes you feel best. If you have a personal concern then by all means this is why the alternative market exists. These products can help those looking of a reasonable option. The other option is considering botulinum toxin injections under the arms to reduce sweat for 6-9 months.