Indeed, beyond being inhospitable, we have expelled whole areas - numerical methods, libraries, and MIS, for example. If we continue this expulsion of the practical we will leave the field a barren husk. The tendency to define ourselves by what we are not is, I think, a legacy of the early days of the field when many were concerned about being seen as merely programmers for the real scientists. We were not just programmers. Sadly, echoes of this outdated fear are present in the title question itself.
Some people seem to think one answer is more respectable.
In truth, we will not be more respected because of what we call ourselves. Let's remember that there is only one nature - the division into science and engineering, and subdivision into physics, chemistry, civil and electrical, is a human imposition, not a natural one. The fact that other disciplines have chosen to build those walls is a failure that we are not required to emulate. Evidence abounds for the value of the interplay in our field between the science and engineering, the theory and practice, the basic and applied. The most theoretical aspects of complexity theory are motivated by the most pragmatic of concerns, performance.