EDIT: If all field theories, irrespective of whether it is renormizable or not, are regarded as effective field theories. The question is addressed here but there is still a confusion. I was told that gauge symmetries must be broken spontaneously because that saves the renormalizability of the theory. Does it not mean that one still prefers a renormalizable theory? If renormalizability is not a severe problem then why can't symmetries break explicitly by explicit symmetry breaking terms?
Renormalisable theories are not preferred more than non-renormalisable theories. We use the former because non-renormalisable interactions are irrelevant, and when we build a model, we always omit those variables that are insignificant to the fit.
Or put it another way: Nature is not a QFT. There are not "correct" vs "incorrect" interactions. We use interactions only if they serve us to correctly model the observed phenomena; and non-renormalisable interactions are (in general) useless for our model: they have no measurable effect in the range of energies we perform experiments.