You are right: the NVIDIA GPU is currently required to turn on the Anano processor. However, this does not stop you from running Theano - it works great on the processor.
The current Anano GPU implementation is based on CUDA, and this requires an NVIDIA GPU. A new development, based on OpenCL, is under development, which should provide work on GPUs other than NVIDIA, but this implementation is incomplete and still practically not useful.
The CPU implementation will work fine. In many ways, this is easier to use than the GPU implementation, and if you use OpenMP, you can still work quite well using many processor cores.