What would separate magic and science so much that neither acknowledges the existence of the other? I suggest this hangs on the nature of magic itself. Magic as it appears in most fantasies functions like a form of super-powers. Example: wizard points her wand at cowering victim and a bolt of purple lightning zapped victim into a neat pile of ash. If magic was like that there's no way science could ignore its existence.
Also readily reproducable magic could be studied, eventually the mechanisms for magic would be discovered, then magic could be improved and upgraded. Leading to a civilisation where magic and science would work hand in hand transforming our world for good or evil.
The way magic operates in traditional societies (this means pre-industrial pre-scientific, and pre-modern) was more like this. A tree falls on Fred's house and no-one's hurt. That's an accident. Just nature at work undermining the tree so it fell down. If the tree fell on Fred's house killing him. Now that's sorcery. When unexpected events harm or kill people, then malign intent must be behind them. The sorcery expresses malign intentions, but it may turn up in unexpected and unanticipated ways. Perhaps even the sorcerer cannot predict what will happen. This is quite unlike magic operating like default super-powers.
What a sorcerer might do is perform a ritual and then sometime later harm will come to the intended victim. For example, sorcerer writes Fred's name and the word DIE on a piece of paper and burns it. Two years later Fred dies of a heart attack or it could be his wife who dies instead. Later Fred dies from despair and a broken heart. This isn't the same as Fred dropping dead straight after the ritual.
This model of magic suggests by its very nature magic may be wilful and contrary. So if scientists suspected ritual magic was real and tried to study it, this makes it impossible to get verifiable results. This is apart from the problems in trying to their research approved by the Ethics Committee. Perhaps if the magic they tried to test only was aimed at producing beneficial results. Like poor Fred winning the lottery (his luck had to change eventually).
Anyone who looks at what magic was like historically or how it is perceived by societies studied by anthropologists will soon realise these traditional forms of magic were and are rarely susceptible to scientific study. Magic is often very different from how it is presented in fantasy.
This provides an answer to why scientists would ignore magic. Its influence in the natural world is invisible and not very different from chance outcomes. Also, people who believe in sorcery are obviously deluded because they believe their spells, incantations and rituals can influence the course of events.
Now for the other part of the question: why don't magic users study science, perhaps with the object of improving their magic, or just understanding magic better? I admit this isn't the strongest reason, but here goes. Perhaps there is something about the scientific worldview that undermines the practice of magic. Once a sorcerer studies and thinks of the nature of the world scientifically, this means they can no longer work magic.
Actually this might go the other way too. Any scientist who fully embraced a magical worldview might be unable to do science well. This also means scientists who believed in magic and wanted to study it scientifically would be rubbish at research into magic (as scientists).
This means I've come up with two answers (not what I intended doing, but sometimes the magic works by itself). One, the nature of magic itself may be such that it can't be studied by science. Scientists would ignore magic, because nothing in nature needs magic to explain it. Sorcerers would practice their magic, but even they might not be able to study how it works. Two, magic and science require mutually exclusive worldviews. This is more than sufficient to separate magic users and scientists into distinct and mutually exclusive communities, each effectively invisible to each other.