Do you think it's wrong of me to tell my girlfriend to become a productive member of society?
Does your gf have a job or responsibilities?
I believe she's completely unproductive and unhelpful not only to society but also to myself
You shouldn't tell your gf those exact words. Be nice and hopefully she will understand the situation.
You don't understand, she needs to wake up and smell the coffee.
Your girlfriend might need to mature a bit and be more responsible. However, telling her in a harsh way will bring more tension between the both of you.