The biochemical similarity of living things fits easily within a creation framework. As biochemist Duane Gish explains:

A creationist would also expect many biochemical similarities in all living organisms. We all drink the same water, breathe the same air, and eat the same food. Supposing, on the other hand, God had made plants with a certain type of amino acids, sugars, purines, pyrimidines, etc.; then made animals with a different type of amino acids, sugars, purines, pyrimidines, etc.; and, finally, made man with a third type of amino acids, sugars, etc. What could we eat? We couldn’t eat plants; we couldn’t eat animals; all we could eat would be each other! Obviously, that wouldn’t work. All the key molecules in plants, animals, and man had to be the same. The metabolism of plants, animals, and man, based on the same biochemical principles, had to be similar, and therefore key metabolic pathways would employ similar macromolecules, modified to fit the particular internal environment of the organism or cell in which it must function. (Gish, 277.)

The claim that all organisms have one or more traits in common is true in the sense that all living things necessarily have the traits by which life is defined, but that is simply a tautology — living things all have the traits of living things.