To answer my own question….
In my opinion, gout cannot be contagious. Because it is only excess uric acid that causes gout. Then, when we lower uric acid to safe levels, gout symptoms stop. So, I think belief in infectious gout is out of date. But, there is one dangerous aspect of infection that we can link to gout.
Gout diagnosis is usually very easy. But, sometimes, a disease can mimic gout. Then that can lead to wrong treatments. As is the case with Septic Arthritis.
I don’t know how many cases of septic arthritis occur each year. But, it is definitely a disease that can be contagious. To explain, I looked at a case where the patient had both gout and septic arthritis. Because it highlights the dangers:
For septic arthritis of the knee, such managements as intravenous infusion of antibiotics, surgical treatment of local tissues affected and immobilization of the affected joint will result in satisfactory effects. In contrast, improper surgical treatment and abuse of antibiotics will worsen knee joint infection, and even cause infection spread and death.
Septic Arthritis References
 Duan, Xiaojun, Liu Yang, and Peiyuan Xia. “Septic arthritis of the knee caused by antibiotic-resistant Acinetobacter baumannii in a gout patient: a rare case report.” Archives of orthopaedic and trauma surgery 130.3 (2010): 381-384.