The stigma against mental illness in America isn't as bad as it used to be. But it still exists. That's why many with mental health issues don't want others to know they have this terrible illness.
If you're disabled with mental illness and can only work part time at a paying job because of it, and you're looking for part time work and you're at a job interview, if the individual interviewing you wonders why you don't work full time at a job, I think it's okay to tell the person that you're disabled due to mental illness. One reason is because the stigma against mental illness isn't as bad as it used to be (like I said earlier). Also, if the individual who is interviewing you doesn't want to hire someone with mental illness, then you probably don't want to work for him/her anyway, in my opinion.
Instead, you want to work for someone who doesn't discriminate against those with mental illness and someone who isn't ignorant enough to believe that all of those with mental illness are crazy and bad people.