___The better question is to ask whether or not the categories "mass" and "energy" are absolute or absolutely mutually exclusive. The properties of light seem to lie somewhere in between. Some refer to a wave-particle "duality", but it might be better to talk of a wave-particle "ambiguity". Light may be better described as neither energy nor mass, but something in-between or encompassing both. How to deal with this matter is a philosophical question as much as a scientific question.
___Consider this, an old question in philosophy: Is the universe one thing or many things? If you answer "one thing", then all the distinctions and differences in the universe are illusions. If you answer "many things", then the connections in the universe are all illusions. Questions of quantity do not allow for ambiguous answers, and it would be hard to make sense of the answer, "well, sort of one thing, but also sort of many". But both unambiguous answers lead to absurd, skeptical conclusions.
___Consider this: by any usual proceedure of assigning properties to things, gravity is a property of all material things. Even Newton referred to it as such. But with respect to this one property, every material thing extends to infinity, and occupies the entire universe, though at different "densities" at different locations. This is a messy universe, so Newton stipulated that we treat gravity as a separate entity, an "invisible force" (a "thing" that is unlike other kinds of physical "things"). Treating it separately allowed him to figure out the math. But this stipulation, how are we to treat it when we talk about the way the universe really IS?
___Material objects are in some respects plural and distinct, and in other respects not-plural, but integrated in a universe that is in this respect "one thing".
The situation is more complicated than can be handled within the mechanics of the language of a "simple" question. The question "Is the universe one thing or many things?" asks for either "one thing" or "many things", and cannot handle the complexity of the answer.
___Now we can sort it out with a more complicated answer, like the "in this respect..." answers above, but then we are left with the problem of whether "this respect" is absolutely, unambiguously distinct from "that respect". Or put another way, whether "this property" is absolutely, unambiguously distinct from "that property". They may be conceptually distinct (color is distinct from mass or taste or solubility), but when has anyone ever been able to separate color from mass in a physical separation?
___Humans evolved in this world, and our senses evolved according to the requirements of getting food, etc, in this world. We and other animals "fortunately" evolved at a non-quantum scale, we evolved at a scale at which material bodies are relatively stable and at which molecular forces determine fixed boundaries for material solids. Our bodies are also made of molecules, and do not slip through the molecular boundaries of material solids. Further, at our scale, light reflects off of molecular boundaries, and we have eyes that are themselves molecular constructions that are affected by the light that hits them. And the spectrum of radiant energy that we see, just "happens" to be light of the wavelengths that reflect off of molecular boundaries of matter, and not the radiant energy that passes through them. (Otherwise, all solid things would be transparent or translucent with regard to some "colors".)
___And with respect to gravity, we don't experience it as an impenetrably-bounded thing, but a contextual element within which we can sense our orientation (balance).
Our senses simplify physical reality for us, and to some degree, disambiguate it for us. We only sense the distinct boundaries of things, and do not sense them as connected.
Though, if you want, you can spend a day imagining that everything you "pick up" is a part of the planet, whose elastic connection to the planet you are merely stretching, until you let go, as if it were connected by some slippery bungee cord to the earth's center of gravity. This conceiving would be as accurate as the usual one, but not very efficient in terms of getting things done.
___So don't be bamboozled by ambiguities like that of light. Our simple senses and minds can't comprehend all the complexity of the world when we take it on "all at once", so we break it into manageable, intelligible, unambiguous units. Accept the limits of human cognition, and accept that the world is complex, not just in terms of the accumulation of a lot of little details, but in terms of the connectedness that makes it seem "ambiguous" to us disambiguating beings.
___The world is as it is, and it doesn't have to conform to the requisites of our intelligibility for it to exist.