Why are operations research departments usually separate from mathematics departments? The title says it all. When I look online, they are usually separate departments
Choose from : history, habit, snobbery, tribalism ...

There is no logical reason for one choice of departmental structure over another. Just look at how often universities change their departmental structures. 

If you bring some groups of people together in a named department then you are excluding other people whose work does in fact have a lot in common with the first group. Departmental structures are always compromises.

Most academics see the benefit of interdisciplinary work, but universities, on the whole, like the apparent orderliness of clear departmental structures.

As to the specifics of operational research: its history was in dealing with urgent practical problems in wartime. Its practitioners were applying mathematics, but were not pure mathematicians. Neither were they what many universities described as applied mathematicians, although in the natural meaning of the words they were, of course, applied mathematicians.

When I took a master's degree in OR in the 1970s, I was in the faculty of engineering. A very few years later, I would have been in the business school of the same university (with the same teachers).