Docker can be configured to be extremely secure. It supports all of the major Linux security technologies, including; kernel namespaces, cgroups, capabilities, MAC, and seccomp. It ships with sensible defaults for all of these, but you can customize them and even disable them.
Over and above the general Linux security technologies, Docker includes an extensive set of its own security technologies. Swarm Mode is built on TLS and is extremely simple to configure and customize. Image scanning can perform binary-level scans of images and provide detailed reports of known vulnerabilities. Docker Content Trust lets you sign and verify content, and Docker Secrets allow you to securely share sensitive data with containers and Swarm services.
The net result is that your Docker environment can be configured to be as secure or insecure as you desire; it all depends on how you configure it.