Barbara, since your ancestor's exemption appears on a report from a State militia enrolling officer, then the exemption likely refers to exemption from militia service. I have a similar list from here in Arkansas (home guards rather than State militia) that mentions exemptions from State service for men who were physicians and "ministers of the Gospel" and one man who provided a substitute.

I don't believe I've ever run across a State militia record that listed exemptions granted by the Confederate War Department.