Assuming freedom to choose whichever currently available GPU is most suited for the job, is it currently feasible to do GPU computation (either CUDA or OpenCL) on Linux using one of the open source GPU kernel drivers (i.e. not fgrlx or nvidia's binary driver)?
Not really. And it won't be supported for the foreseeable future. They still have so much work to do with just the graphics part that there is no time to develop the computing stack.
I personally relate to the closed drivers as I do to the actual HW, I cannot change the HW so I don't mind that I cannot change the drivers. Even though the closed drivers tend to be rather buggy and it takes ages for them to support new kernels and new X.org.
sharpneli already provided the right answer. However, I would like to also point out this article which indicates that there might be a change in thinking at least from AMD. But that will most likely take several month (years) before we will actually see a real open source driver that runs OpenCL.