Is it common for research disciplines to have a large gap between theory and practice? TL;DR: Is it normal that the theory sub-community and the applied sub-community of a single research field to have different goals and different standards for peer review - to the extent that the research field itself suffers?

I work in a subfield of computer networking. During the last two years I've been in a quite unusual position (for the subfield) as a person whose job was to bring some mostly-theoretical results of big research project to practice. Personally I've greatly enjoyed this role; however, the job also brought a lot of frustrations. It seemed that neither the theory people nor the applied people are particularly interested in a work that bridges these two sub-communities.

In general, there is a very little overlap between what the theory subcommunity cares about and what the applied subcommunity cares about. To give one example, the assumptions made by the people in the theory camp often are wildly wrong. In my opinion, that renders most of their results quite useless; however, they do not spend a lot of effort trying to recognize and correct these invalid assumptions, as it's possible to publish their results anyway, especially in sub-premier conferences. On the other hand, I feel that applied conferences in the field are resistant to novel ideas; a paper that simply demonstrates how to achieve state-of-art results a different approach is not recognized as novel enough. In my opinion, the typical top-level applied paper is therefore quite boring; due to the peer-review standards, they must focus on the engineering work and on applying known ideas to existing problems, rather than on novel ideas and novel problems.

To give some other anecdotal examples:


after I reported that a specific algorithm (developed by one of my
theory-oriented collaborators) does not seem to give good results on a
real dataset, I was suggested that "maybe we should evaluate it on
synthetically generated data instead";
in a different conversation, a senior applied researcher commented
that "we skip over any mathematical parts when reviewing a paper".


To me it seems very likely that the progress in the subfield was faster if both communities were working closer together. The objective of science, after all, is not to simply produce more papers; it is to discover more knowledge.

Are other disciplines facing a similar problem, and how do they deal with it?
Significant splits between theory and practice, such as you are describing, are not at all unusual.  What many people fail to recognize is that research spanning between theory and practice is effectively interdisciplinary research!

Moreover, what you call "theory" others may call "applied" and vice versa.  I have noticed that whether I feel like the "theory person" or the "applied person" in the room depends strongly on which community I am participating in at the time. In fact, what you are experiencing is only a small part of the theory/application spectrum.  Many funding organizations attempt to quantify the theory/application spectrum with some sort of technology readiness level rubric, and you are almost certainly experiencing only TRL 1-3 communities, as that is where almost all academic research lives.

Why this matters, and why there is a gap in communication between communities, is that the problems encountered and solutions required at different TRLs are often fundamentally different.  At one end of the spectrum is: "Might this be plausible?" and at the other end is "How much does it cost to get one shipped to me by Tuesday?"  All of the questions on this spectrum can be valuable, even if some seem "farfetched" and others "boring" to you based on where you personally happen to be sitting on the spectrum right now.

Spanning different levels is difficult, and to do so you will need to figure out how to speak the languages of the different communities.  If you are able to do so, however, it can be of great value both to your career and to the larger communities in which you live.