Well,
Since I have been gainfully employed for many years now, I have not had the need to compose a resume or fill out a job application. However, I happen to own the company that I work for, and in my position I see the job applications and the resume of every person who comes to me for a job. Not long ago, a fellow who put in an application mentioned in his resume that he was involved in the "9/11 truth movement". He further confirmed this fact in person during his interview. At that point, the interview was stopped, and he was shown the door. Words, actions, and the people/organizations a person chooses to associate themselves with can have real world consequences.
L.
P.S. Do you list "truther" on YOUR resume and various applications?