As much as I understand the renormalization group transformation and the concept of relevant/irrelevant operators, I'd say that if we push the reasoning of only looking at relevant operators when we follow a "renormalization group orbit" (a curve in the space of the parameters) to the infra-red regime the other way, so going to the U.V., we should keep all the operators this time (as they are no more suppressed by huge factors), or there is a infinite number of them, depending on an infinite number of the derivatives, and we end up with a non-local theory. As this reasoning can be applied to every QFT, does this mean that they are all non-local in the U.V.? or the reasoning fooled somewhere (breakdown of the QFT framework somewhere for example...)?
Quite on the contrary, every genuine and genuinely consistent QFT is exactly local in the UV; it must converge to a scale-invariant theory, a fixed point.
One may obtain nonlocalities in the IR for most theories (through the higher-derivative corrections with arbitrarily many derivatives) – if we compute the effective field theory description of the dynamics, either directly from the exact UV starting point, or otherwise.