I'd look at products similar to this: https://www.usg.com/content/usgcom/en/products/walls/drywall/drywall-panels/mold-resistant-panels/sheetrock-glass-mat-panels-mold-tough.221720.html

Consider Trusscore or similar panels.

Basement moisture is often due to condensation on cold foundation walls especially if a wall has been added over it preventing conditioned air circulation at the face of the wall.

Proper exterior waterproofing, insulation and drainage are best but sometimes spray foam on the interior of the basement wall works.

Metal studs will work with the proper screws but how would you finish cement backer board?

"Mold only needs moisture." Mold needs not only the right moisture conditions, but temperature within the required range for propagation, and a food source. Fiber-cement panels are constructed from wood fibers and cement. Fiber-cement will absorb moisture and the wood fibers can serve as a food source for mold. By itself, use of fiber cement panels is no guarantee against mold formation. A better, preventive, approach is proper waterproofing, insulation and drainage as noted by res2 above. Those will allow a greater range of interior finishes to be used.

Fiber-cement contains wood fiber reinforcing but concrete backer boards are reinforced with fiberglass mesh facings. Using the term cement board can be confusing.

Agreed. That said, concrete backer board wouldn't typically be considered a finish material. If the OP is considering the use of the product in lieu of sheetrock, I assume it's intended to be a finish material.