Well, if you look at Newtons law for gravitation and Coulombs law in electromagnetism, they look similar and hence we could ask why are two such different phenomena governed by the same law?
One answer that is certainly correct but not very satisfying is to say that physics uses mathematical models and its quite possible that the same mathematical model is used in very different models.
A more satisfying answer, is to suggest that the inverse square law is due to the dimensionality of space.
Another satisfying answer which opens up many other questions amd not always many answers is that they have a common root. This is the way of unification which has been successful in unifying three of the fundamental forces. But only after two centuries of continual effort.
Given that QFTs are used in both condensed matter and fundamental physics we can propose two possibilities in analogy to the ones above. Either we say that QFT is merely a mathematical model useful in two very different physical domains and this does not point to anything deeper; or in the contrary, we can say that this does. Obviously the latter suggestion is more intriguing.
First, in applications of QFT to condensed matter its important to note that the quanta here do not describe elementary particles but quasi-particles, or collective excitations. I think it is also accurate - but since I'm not a condensed matter theorist, take this with a pinch of salt - to say that QFT here is done in Euclidean signature rather than the Minkowski signature used in fundamental QFTs.
Personally, I think that this indicates that QFT is not a fundamental theory but an effective theory - only valid upto a certain range of energies. And that a deeper theory is required.
One suggestion is string theory, on which the jury is still out on (not least because it predicts an infinite tower of massive particles none of which have been seen). Here we see elementary particles as collective excitations of the underlying stringy world just as we see condensed matter quasi-particles as collective excitations of an underlying atomic world.