I do include alcohol. A very large percentage of violent crimes are committed under the influence of alcohol and a known alcoholic should not be carrying a gun.
And yes, there are exceptions to every right. These are dictated by common sense, common decency and human conscience. Rights are not license to do as one pleases and damn the consequences. Rights exercised irresponsibly will be lost - witness what has been happening in the United States of America. An amoral or immoral, irresponsible and ignorant people will not keep their rights and it does no service to anyone to insist that we must allow unlimited exercise of every right in any circumstance. That way lies slavery.
You do realize how subjective the determination of "alcoholism" is, how easily a government employed doctor could make that diagnosis, and how difficult it could be made to get it changed?
And you're proposing giving the bureaucracies of the federal government the authority to determine who they can make exceptions for, on the premise that it will be done according to those criteria?