Do we have to fix parameters by experiment when using the renormalization group? In traditional renormalization, renormalized masses have to be fixed by experiment before going on to make other predictions. Do renormalization group methods, like Wilson's, require fixing parameters by experiment as well?
 A: This has little to do with renormalization or the renormalization group. It has everything to do with the fact that the theory has adjustable parameters.
As an example, consider the standard model of particle physics, in which the masses of the charged leptons all come from their Yukawa couplings to the Higgs field. The values of those Yukawa couplings are not constrained by the structure of the theory (e.g., symmetries), so the best we can do is choose their values to make the theory's predictions match experiments. This is true no matter how we're using the theory to do calculations -- whether we're using perturbative renormalization or Wilson's renormalization group or whatever. The only difference is in the details of how we connect the theory's adjustable inputs to the experiments that fix them.
If we have decided to keep the theory renormalizable, then it only has a finite number of adjustable inputs that need to be fixed by comparison to experiment. After that, no freedom remains, so the theory's remaining predictions are either right or wrong — if we insist that it be renormalizable. We can also consider non-renormalizable theories, as long as we maintain a finite UV cutoff as a substitute for the unknown higher-energy physics. The number of adjustable inputs is still effectively finite if we only count inputs that make a significant difference at low energy. This is the Effective Field Theory perspective that we have in mind when we make the standard model nonrenormalizable by adding terms that account for neutrino masses and gravity.
