There are a variety of health requirements to become a permanent US resident. Having been through the process I can confirm that it is a very long, frustrating and bizarrely complicated procedure.
The medical requirements are actually one of the simplest steps.
You need to show evidence of immunization against the following diseases: Mumps; Measles; Rubella; Polio; Tetanus; Diphtheria; Pertussis; Influenza Type B and Hepatitis B
This all seems sensible and is nothing more than is recommended in the US (and required if you want to attend public school).
You also need to show you don't have Tb. As I mentioned if you have already had the Tb vaccine then the simple skin test will come back 'positive' for Tb so you have to have a chest x-ray.
Finally you need to give a blood sample that is tested for two specific diseases: AIDS and syphilis. They may also test for others but I believe they always test for AIDS and Syphilis. This also seems fairly sensible since with both diseases people can be asymptomatic for a long time whilst continuing to transmit the disease.
Even if you test positive for any of these diseases you can apply for a waiver. The most common communicable diseases for which waivers are sought are tuberculosis and AIDS. A waiver applicant with tuberculosis must agree to see a doctor immediately upon admission and make arrangements to receive private or public medical care.
An HIV+ waiver application must include evidence that 1. the danger to the public health of the United States created by his or her admission is minimal; 2. the possibility of the spread of the infection created by his or her admission to the United States is minimal; and 3. there will be no cost incurred by any level of government agency of the United States without prior consent of that agency. HIV+ applicants will also have to show the following: 1. medical treatment has been arranged in the United States; 2. the applicant is aware of the nature and severity of his or her medical condition; 3. the applicant has provided evidence of counseling; and 4. the applicant has demonstrated a knowledge of the modes of transmission of the virus.