The Noah and Gilgamesh stories have similarities and differences.
Yes, true, there are similarities and differences between Noah and the Flood story of Utnapishtim (in the Epic of Gilgamesh).
But why do you insisted on talking about science in the next sentence, when you don't have to...ESPECIALLY when you don't understand how to the scientific procedure work.
Your ignorance with all sciences, but that you make incorrect claim of something you don't understand, is like you taking a stroll in the minefield.
For instance, in your next sentence, you wrote:
Religious anthropologists use the scientific naturalistic methodology approach and presume no supernatural story is correct and use the theory that one story was copied from previous stories in all cases.
Please note what I've highlighted in bold & red.
You are talking about the "scientific approach", and you had brought up "naturalistic" (eg "scientific naturalistic methodology approach"), which means - when use "scientific methodology" and "naturalistic", it means use science on NATURE, hence it would relate to Natural Sciences.
You know what "nature" mean, don't you?
Natural Sciences is about the studies of nature, like astronomy, physics, chemistry, biology (eg anatomy, physiology, genetics, evolution, etc), studying the Earth (eg climates, atmosphere, mountains, rivers, natural formation of terrains, geology, ecology, etc), and so on. Natural Sciences are anything that's not man-made.
Now if you know what anthropologists do for living, the study of anthropology, then you would know that the main focus of anthropology, is the studies of human societies, human cultures, human history (plus archaeology), human social interaction, etc, all of which involved studies that fall under the Social Sciences category.
Social Sciences are not Natural Sciences.
Anthropology might or probably delving into humanistic disciplines, like art, philology (study of languages), literature, religion. Humanistic isn't Natural Sciences.
In the non-highlighted part of your paragraph, you mentioned stories.
Stories, like Flood myths in the Epic of Gilgamesh and in Genesis story relating to Noah (Genesis 6 to 8).
As a literature, both stories fall under the Humanistic category, not the Natural Science. And it is the same with the subject matters of both stories, that are religious theme, so religions (including theology) would be Humanistic subject, not a naturalistic subject, hence have nothing to do with Natural Sciences.
The Bible and the Epic of Gilgamesh, have more to do with Humanistic than with anthropology, but regardless if you want to talk about anthropology or other Social Sciences, neither of them have anything to do with "natural", hence they aren't "naturalistic".
This is presumption from the start and has to end up with a conclusion that denies the truth of the Bible.
No one is denying that the Bible, including the story about Noah and the Flood, as a work of literature and as a work of religion.
Now, we can look at it (both the epic and Genesis), from philology or literature perceptive, as to which is older.
There are no doubt, the Mesopotamian version is older. The Epic of Gilagmesh dated all the way, and scribes have copying the Babylonian and Assyrian versions, since the Old Babylonian period, which is the 2nd millennium to 1st millennium BCE, known in both Mesopotamia and Levant as the Middle Bronze Age (c 2000 - c 1590 BCE). The Epic of Gilagmesh is very popular during the Middle and Late Bronze Age, because clay tablets about Gilagmesh were found in far west as Hattusa (Hittite capital), Ugarit (now Ras Shamna), Amarna (Egypt) and even in Canaanite Megiddo, during the mid-2nd milllennium BCE.
There are also the Epic of Atrahasis, Atrahasis being another name for Utnapishtim, is dated to 17th century BCE, but even older is the Eridu Genesis, written in Sumerian, where the hero is originally name Ziusudra.
This Sumerian tablet (Eridu Genesis) is badly damaged, and only portion of the text survived, but enough to know Ziusudra predated the Old Babylonian Atrahasis and Utnapishtim. And it is dated to the 2nd half of the 3rd millennium BCE (meaning somewhere between 2500 and 2000 BCE).
All version of Mesopotamian flood myth, predated the writing of Genesis, which you cannot find before 6th century BCE Exile at Babylon.
Regardless of any story, Hebrew or not, what Noah's story isn't, it isn't science.
For instance, there are physical evidence in archaeology or geological evidence (flood deposits) in any later of rocks that are widely found in one period of time, so no evidence of global flood.
If there were global flood as in the magnitude of Genesis 8, where waters covered all the high mountains, including Ararat, there should be flood deposits everywhere in the world, that would point to a single "DATE". There are none.
Yes, there have been massive flooding in the past, but none of them covering mountains, and none of them in human history ever happened on global scale.
Flood on massive scale, always leave evidence behind, not destroy evidence.