Final answer:
The non-controversial application of recombinant DNA technology among the options provided is Metagenomics. It studies environmental genetic material and is less ethically problematic compared to genetic modification, biological weapon development, and genetic screening.
Step-by-step explanation:
The application of recombinant DNA technology that is NOT controversial is C. Metagenomics.
Metagenomics is a field of genetics that involves analyzing genetic material recovered directly from environmental samples. This approach to genetics allows scientists to study communities of organisms directly in their natural environments without needing to culture them in a lab setting. Unlike genetic food modification, biological weapons development, and genetic screening, metagenomics does not usually involve ethical dilemmas related to altering the genetic fabric of living organisms or concerns with privacy and misuse.
It's primarily focused on understanding the diversity and function of microbial communities which can lead to advances in biotechnology, medicine, and environmental science without the direct ethical concerns tied to the other applications.