Realtime is a complex question. There is super-hard realtime, with ironclad guarantees of sub-millisecond (sometimes microsecond) response times, and guaranteed performance (such as throughput). That's the realm of dedicated hardware. Things like Arduino is the amateur low end; vehicle control, FADEC, industrial control, medical devices, military hardware, and data acquisition is the more high-powered side of this. It uses a mix of full-custom software and dedicated real-time OSes. VXWorks used to be the 400-lbs gorilla in this market, but there are many competitors.
Then there is soft realtime, where response times are more in the millisecond range, and missed response is not catastrophic. In the last two decades, Linux-derived systems have made significant inroads in this application. The biggest one I know of used to be RTLinux. Architecturally it is an interesting hybrid, using a dedicated microkernel for the hard realtime part, and then running Linux in a sort of virtualized environment within that microkernel. I know it had considerable commercial success, but there was also a big scandal involving patents (and I don't remember the details of why it became a scandal). I think it has somewhat died in the last few years.
And then there is a whole slew of intermediate solutions. RTAI is one of them, with a kernel module that shields the (inherently non-real-time) kernel somewhat. There are also research projects that are based around micro-kernels or predictable kernels, which then use a normal userspace for cost saving. One of the big deals in this business is development cost, and having the ability to run a stock Linux userspace makes systems self-hosting, which is very convenient for developers.
But to get back to the OPs question: I have heard that some projects were using *BSD components in their work, because the licensing is easier to deal with, and because of the patent brouhaha. But I've never heard of a canned solution that's based on and compatible with FreeBSD. Which doesn't mean that one doesn't exist, only that I haven't heard.