There are linguists that are very much against conlanging, here are two commonly claimed reasons:
The latter reason is also common among non-linguists.
What others are there?
That this currently isn't a field with much revenue (except maybe movie languages) or practical use associated with it has already been mentioned.
I think there is a throwing-out-the-baby-with-the-bath-water dynamic going on with the following triggers:
Crackpots. They exist in the conlang community and seem to be over-represented. Examples include aUi, by John Weilgart. All fields have crackpots, but some fields attract crackpots more than others. Weilgart said he got the inspiration for the language from (real) space aliens. This differs from say, Klingon, where the participants know they are real Trek fans and the aliens are fictional.
Auxlang promoters. Auxlang promoters, in the hopes of gaining followers, make wild claims, in particular claims about ease of learning, cultural neutrality and global utopia (or at least some substantive move in that direction).
Historical philosophical languages turned out to be a dead end as languages and lines of thought. The languages hoped to allow the universe ideas to be divided into hierarchal categories and additive "compound words" in the lexicon and for the grammar to follow some sort of "natural" syntax, i.e. little thought was given to syntax. e.g. John Wilkins's language, although it did inspire Roget's thesaurus. It didn't prove to be more useful (or at least, not more popular) than natural languages for discussing the world or philosophy.
Loglans (like lojban) promised to allow people to say what they mean and people would hear what that person meant. In other words, remove ambiguity in speech. In practice, loglans removed syntactic ambiguity for people who are good at mentally parsing like a machine parser, but left a lot of room for misunderstanding and semantic ambiguity. Loglans also promised to possibly be a way to communicate with machines, possibly for artificial intelligence applications. While a machine can parse lojban, I don't know of any implementations of a "run time" that does anything interesting with the parsed values (say, querying a store of lojban encoded facts, similar to how Prolog words). This doesn't mean loglans are useless, it is just another conlang that didn't deliver on the original promises.
And there is a scholar out there who wrote some remarkably hostile pychoanalytic-like analysis of the mental states of those who create/use artificial languages. I'm really sorry I can't find it.
With red flags like the above, I wouldn't be surprised if people see the field as sort of a quest to square the circle, create a perpetual motion machine, or the like.
I don't agree with them myself. In the field of languages for the profoundly disabled, such as deaf-blind, new things that look like languages are being invented by health care providers and they are doing a so-so or lousy job of it because they don't have any scientific rigor and methodology behind them.
Not sure about being “against”, but I’ve seen some linguists dismiss conlang studies due to a strong form of nativism. Suppose you’re convinced that 1) all languages are variations of an universal, hard-wired human capacity; 2) languages can only be acquired “for real” when you’re a child in the critical period; and 3) the one true goal of linguistic science is to understand Language (defined in these terms). If so, then conlangs would be something like fake data. Natlangs are seen as clues to Language, but conlangs could lead you to wrong conclusions.
Though there are some linguists who express hostility toward conlanging, most notably Yaguello in her book "Lunatic Lovers of Language," I haven't heard of any general outcry from the linguistics community against conlanging. However, I do believe that most linguists consider natural language to be the proper subject matter of linguistics.
As a conlanger, I think that this is as it should be for several reasons.
First, linguists discover, document, and interpret their data. In linguistics, inventing the data is strictly forbidden for obvious reasons. But when I devise a conlang, inventing the data is not only permitted--it is the whole point of my hobby. I think that this makes conlanging something other than a science.
Second, a great deal of theoretical debate in linguistics is devoted to the degree to which linguistic knowledge is innate and to the existence of language universals. Since conlangs are almost never acquired naturally and can be designed with or without any of the proposed language universals, I don't see how the mere study of conlangs could have any bearing on such issues. For example, inventing a language without recursion would not, as far as I know, shed any light on the controversy about whether recursion occurs in Piraha.
Third, although every good conlanger knows more about linguistics than most non-linguists do, conlanging involves making implicit or explicit whimsical or esthetic judgments about linguistic structures that have no place in linguistics. To a linguist, ergativity is interesting and worthy of study. To a conlanger, ergativity might be a cool feature to put in one's conlang, or conversely a trite feature since all the other conlangers are putting ergativity into their conlangs. A conlanger might also believe that copying natural language ergativity isn't weird enough, and might therefore look for ways of conditioning the ergative/acccusative split that don't occur in natural languages. Another conlanger might also think it would be fun to give ergative marking to some hypothetical relative of Latin. For conlangers, there is no limit to the whimsy.
I have often likened the difference between conlanging and linguistics to the difference between painting monsters and studying zoology. There are, I suppose, some zoologists who take an occasional interest in depictions of monsters, but it would not surprise me if most zoologists didn't share this interest.
Creating a language is like writing a novel or creating a sculpture: it can be a fun exercise, and an object of art for people to admire. If you happen to not be into a certain genre, you will probably not be interested in studying it.
I think the same thing applies to constructed languages. I personally do not find them very interesting, with some exceptions, such as Tolkien's languages—but even those I do not find interesting enough to study: I'm just glad they're there, because they make his books and stories all the more immersive and "realistic". (Many other constructed languages, on the other hand, I find crude or unimpressive for various reasons.)
If certain works of art have some sort of physical, historical, or social significance, then that can be another reason to study them. But it can feel like a waste of time if they haven't. I don't like studying a language that I feel I can't learn anything from, as in nothing relevant for how real languages work. This is probably why studying them is normally not a significant part of academic curricula.
