What mouth diseases could prevent you from getting braces?

Braces. Moderate to severe periodontal disease that is uncontrolled could prevent you from braces. There are other. Other body diseases can be a factor in periodontal disease such as uncontrolled diabetes or aids are a couple to mention.
Periodontal Disease. Cavities - someone prone to cavities or with a dry mouth (xerostomia) that leads to increased cavities is not a good candidate. Extra teeth or impacted teeth - need to be removed or guided into proper locations. Uncontrolled periodontal disease can lead to rapid loss of the gums and bone that support the teeth. Short teeth (roots) - some teeth do not develop normal root structure.
None if managed. Braces are contra-indicated in the presence of uncontrolled periodontal (gum) disease, rampant caries (cavities), uncontrolled diabetes, and some cancers. Get an evaluation by an orthodontic specialist, be sure there is no active hard or soft tissue infections in your mouth, that you have no untreated systemic diseases, and then go for it. The results can be spectacular.
Diseases. The most common diseases precluding orthodontic care are active periodontal (gum tissue) disease and caries (dental cavities). Those issues should be resolved before beginning orthodontics. If you have other health issues, those need to be explored through a complete medical history by your specialist orthodontist.
Several. Flourosis and amelogensis emperfecta, in addition to periodontal disease.
I will try to answer. Patients with periodontal disease usually must obtain periodontal treatment before getting braces. A deep cleaning is performed, and further treatment may be required before beginning orthodontic treatment. Bone loss due to periodontal disease may lead to tooth loss during treatment. In some cases, teeth may be loose for a prolonged period of time. One may be able to wiggle one's teeth for a year.