Are people with general anxiety disorder allowed to become physicians? what about other mental illnesses?

Certainly: Are people with mental illness allowed to become a physician? Have you ever met a surgeon? :) seriously, there is no reason why not, as long as the mental illness is controlled. If not, the course of study and preparation needed to follow this path would likely make it impossible anyway. But you could say the same about numerous other professions requiring a lot of study and dedication.

If able to focus yes: Yes, someone with generalized anxiety d/o can become a physician -- as long as symptoms are being dealt with and s/he can focus on tasks at hand. I've treated many physicians with anxiety disorders, and they usually do excellent work with patients. Sometimes their compulsive worry can deplete them, though, and we have to work on that. Depression, panic, ptsd, etc are also common issues.

Treatment: Anxiety is very treatable and does not have to affect a persons career choice. It is important to get treatment though, anxiety can make even the smallest things very difficult. As far as other mental illnesses go, there is no "rule" about it, but oftentimes the mental illness itself will keep a person from getting the career they want. Best wishes and good luck in whatever you choose to do.

Sure.: Anybody who studies and manages their issues can become anything. I know physicians who have far more complicated psychological issues than anxiety.