First off, I am not saying that conlangers are oppressed or shunned or anything by academic linguists. Far from it. It's often said that conlangers have a "persecution complex" in this arena -- i.e. we're whiny little geeks. If anything, conlangers get more friendship from linguists than from the general public. That said, most linguists don't exactly brim over with warmth and welcome for practitioners of the secret vice. Conlanging is typically regarded as a kind of silly little hobby or diversion: nobody cares that much as long as you don't let it interfere with your work.
I will admit that there is one anti-conlanging argument that stings me and makes me feel guilty: "Why aren't you out in the field, saving dying languages? You're squandering your talent, skills, interest, and time!"
This argument seems a lot more valid than its generalized counterpart, "Why aren't you working against Great World Evil #42373?" Linguistics interest and expertise are relatively thin on the ground, so it's harder for the cause of saving dying languages to get enough resources/people behind it. Conlangers are often so interested in linguistics that they pursue their interest even when it harms other aspects of their life. Not for nothing do people call it addictive.
But seriously? Firstly, most conlangers just don't have as much spare time as people seem to imagine. Secondly, and more important, most conlangers don't have the expertise to do linguistic fieldwork. A goodly number pursue linguistics in college, but you need a lot more than a bachelor's to do fieldwork. I only know of two conlangers who are linguistics grad students (undoubtedly there are more, but not many more). Most of us have day jobs. We're hobbyists. Would you want model-airplane hobbyists fixing fighter jets?
The other main arguments against conlanging are that it's frivolous, pointless, a waste of time, etc. And for this I can't do better than to point you to The Conlanger's Manifesto, by David Peterson, which eloquently defends conlangery as an art form:
...Looking only at the utilitarian end of it, if the creator isn't going to use his/her language for communication, and since language can be viewed only as a means of communication, language creation is pretty useless.
But is this all language is: A method of communication? If so, what is poetry? what is literature? What possible use could James Joyce's Ulysses have? I suppose if you were on a desert island and needed to smash crabs, it would do the trick—it's pretty thick, after all. But beyond that? According to them, it would have no use. And why stop there? What good do paintings do anyone?...Pretty soon what you're left with is a world without art.
At this point, the argument should come to an end. The rigor and usefulness of art is an argument that has been argued many times by many people much more articulate than I, and by now (I certainly hope), the whole world should have figured out that art really does pull its weight on Earth.
Amen, brother. Conlangery is the art of linguistics, and it should need no more defense than that.
Occasionally, you'll run across linguists actually using conlangs. If you're teaching a linguistics course, occasionally you may want to illustrate some particular concept by using a conlang. That way, you can design the conlang to show off the feature to its best advantage, and avoid all the irrelevant noise/irregularities that you'd get if you used a natlang. It's the same principle as medical illustration: realistic, but with all the fat trimmed away. Just try and find an illustration that shows the pancreas without trimming away a whole load of other viscera! It's damn near impossible. Conlang examples serve the same purpose in a linguistics class. The goal is transmission of key information, not pinpoint-accurate naturalism.
Another, less-used, possibility is to have students create a miniature conlang that exemplifies a particular feature. I've seen a worksheet that taught the basics of ergativity very effectively this way. Unfortunately, it wasn't from an actual linguistics class. It was from a presentation at the 2nd Language Creation Conference. Er, I mean, a presentation that never took place (it was sacrificed in favor of another panel discussion due to time constraints): "Applications of Conlanging in Pedagogy". You can see the worksheet on page 13 of the PDF of the program. I can't genuinely speak from the perspective of a student, because I already knew what ergativity was at the time, but I really think it would have been very effective as a homework assignment, because it gets you actually working with an ergative system.
But the most interesting intersection of conlangs and linguistics, in my opinion, is in the domain of research. A lot of studies have come out recently, where people are exposed to a small conlang and then their learning success is tested and studied. This is a really exciting paradigm, because you can engineer your language to have certain traits in the area you're interested in, and to be `normal' or `easy' in all other areas. If you're testing acquisition of (say) verb-subject-object word order (English is subject-verb-object), you can make your language have perfect consistent VSO order and be completely unremarkable in everything else. Good luck finding a natlang that fits that bill. It's the same cutting-out-the-noise principle we saw earlier.
Or, if you want to put in noise and study how people will deal with it, you can manipulate the type and amount of noise to a very high resolution. Likewise with (say) syllable-transition probabilities in a word-segmentation study (if ba is always followed by ka, but ka is followed by a whole lot of different things, you can deduce that fooBAKAbar is the words fooBAKA and bar, not fooBA and KAbar.)
I'm currently involved in a research project using this paradigm, and I think it's an incredible tool. Look out for a lit review in the near future!
There are some conlangers who would like to see descriptive research done on fully-fleshed-out conlangs. And I hate to say this, especially because I'm good friends with this crowd, but I disagree. I don't think that investigating and describing conlangs can tell you much about the range and properties of human natural language. (Most academic linguists, I think, would agree with me.) To find out anything about human natural language, you ought to study human languages that have evolved naturally, instead of ones that were consciously invented. You can make a conlang with any conceivable twisted logical structure; the structure may be possible, but that doesn't mean it would ever evolve naturally, or that it's reflective of anything in natural language.
But since conlangery is the art form associated with linguistics, you could do the same sort of humanistic or aesthetic studies that you do on paintings (the art form associated with vision science). What do people find elegant or appealing? What conlang properties elicit what subjective reactions? What bizarre structures have what bizarre effects on people trying to use the language (the linguistic analogue of optical illusions)? And this could have implications in the study of natlangs.
Next up: the learn-a-conlang paradigm in language acquisition research.