Multiple FFT backends?

[Keno]

I'd like to revisit @stevengj's pure Julia FFT code (@YingboMa has an updated copy at https://github.com/YingboMa/DFT.jl) - primarily because I'd like to extend it for ffts over finite fields. However, it's a bit awkward at the moment to have multiple FFT packages that all extend the AbstractFFT APIs, since there's only one entry point for a given array type. How do we want to handle this situation? Does it make sense to pass some sort of backend token to all the APIs that the implementation can then dispatch on? Any other suggestions?

[mkborregaard]

Is it correctly understood that this issue means that no packages can depend on e.g. FFTW for internal (non-exported) functionality, because that would break the FFT workflow for any package user having a different FFT package loaded?