Question: There are linguists that are very much against conlanging, here are two commonly claimed reasons:

1. It's not science.
2. It wastes manpower, time and energy that should have been used to
rescue an already existing rare natural language or do field work.

The latter reason is also common among non-linguists.

What others are there?

Answer: 
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.