I have had success running Debian 9 (Stretch) on the CI20 with the 3.18 kernel provided by Imagination Technologies before they stopped supporting the product:
I used some of my own tooling that invokes multistrap to make the root filesystem, finalising the initialisation on the device itself. There were some problems doing this with Debian 8 (Jessie) involving systemd and package incompatibilities, but these seemed to have been worked out when Stretch came around.
There is an ongoing effort to target the mainline Linux kernel with the necessary drivers for the CI20:
Of course, there are mainline kernel contributors who have already provided much of the support for Ingenic SoCs, but the peculiarities of the CI20 need attention with respect to configuration and some drivers. For instance, the HDMI output should already be supported in a mainline driver (Synopsys DesignWare HDMI), but this driver needs specialising with some extra code for the JZ4780. I have written this extra code, but then it needs to work with the DRM (display) driver, and this needs enhancing for the JZ4780 (which I have also done, for the most part), and then everything needs to be "wired up" and persuaded to work, which has proven to be a challenge.
I have also run the Fiasco.OC microkernel on the CI20, since it was mostly supported already and needed just a bit of extra work, and I have even written/ported some drivers to the L4 Runtime Environment which runs on top of Fiasco.OC (including the start of the HDMI driver and the display driver, enough to get a picture). But that only provides the very beginning of a system: in other words, it cannot be used for anything practical.
I never found much out about the BSDs for the CI20. I guess that some other systems could be ported to it: HelenOS might be a candidate, and Inferno might be a possibility. Porting things are not necessarily low-intensity activities, however.
Paul