Starting on page 7, the Georgia state form has a section for Profit Sharing. If a member withdrew from the club, their percent shows zero. Isn't this a problem because it means the state will assume the partner had no profit sharing for the year?

Investment income is sourced at the partner level and not the partnership level. As an investment partnership receiving all of its income from, buying, holding and selling publicly traded securities you have no GA source income. Thus the zero amount for a member on the GA tax form for GA source income.
However, your members do have to report their share of investment income on their personal GA tax returns. It may seem unusual that this income is not GA-source for the club but it is for GA residents of the club. This is just one of the quirks of investment partnerships and investment income.
The member (or their estate) would use the figures on the Federal K-1 for their share of the club's investment income. The club should also give a copy of the withdrawal report for their withdrawal.