Science studies uniformities. There is uniformity in the physical universe and science is the study of that. In addition to uniformity there is uniqueness in the universe. One can study that, and apply science to understand it better but science does not study uniqueness per se. Other disciplines deal with aspects of uniqueness – history, philosophy, theology, and literature for example.
One does not need a principle of uniformity – that nature is uniform – in order to do science. Behind a principle of uniformity is a logical point as to the nature of induction. John P. McCaskey has explained this and is writing a book on the topic. I have written before on this topic here.
A uniformity principle implies that the future is like the past but cannot say which past properties imply which future properties. That is what induction does: it classifies things that share essential properties, whether in the past or future. Inductive classification is needed, not a principle of uniformity.
Science need not affirm that there is only uniformity in the universe or that nature is only uniform. That was understood before the late 19th century, when naturalism was promoted by TH Huxley and others as the only way to do science.
Scientists should say that the science of biology covers the uniform part of biology and the rest is handled by others. But scientists assert that the science of biology covers all of biology, which is false unless one accepts naturalism or defines biology as the study of those aspects of organic life that are uniform.
Science studies uniformities. Uniqueness also exists but science is not the study of that. One can be open to what is unique, non-uniform, or mysterious and do science.