What are a few programs that can prepare undergraduate students for the foreign service that do not require citizenship status?
The U.S. Foreign Service does not require U.S. citizenship. To test out this area of work and prepare for a potential career in the foreign service I would encourage you to participate in volunteer programs abroad to gain experience. You could do programs that are shorter (there are many organizations that offer "voluntourism" trips), or longer tours abroad like the PeaceCorps (2 year placement) or 1-year teaching programs abroad (I did one through an organization called World Teach but there are many). Thinking Beyond Borders is another great organization. I did my first volunteer trip abroad once summer in high school and raised money for it from the local Rotary Club. I wrote them a letter explaining why I wanted to travel abroad to volunteer and asking for a grant to support it.