The question as to whether Docker is required to run a peer, orderer, fabric-ca, etc. depends on what effort you are willing to expend.
The Hyperledger Fabric community publishes stable, tested Docker images for X86, PowerPC and s390 (mainframe) architectures for each of its releases. These images are based on Ubuntu.
To use the Hyperledger Fabric published release images, you need Docker and some form of orchestration support. For sample use cases, we provide some simple Docker Compose definitions. Hyperledger Cello and other provisioning platforms such as the IBM sandbox, provide kubernetes helm charts.
It is possible to build the binaries outside of their Docker images without modification of the source. However, if you wish to build for an alternative OS (e.g. Windows, RHEL or CENTOS, etc) then you will need to modify the build process. However, it can and has been done. Suggest you reach out to the hyperledger-fabric@lists.hyperledger.org mailing list to see if any in the community that have built for alternative deployment will share their work.