Is it common for research disciplines to have a large gap between theory and practice?
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.