This comes under the category of “pet hate”, I have to admit, but also it’s a question of getting the science right (more on that another time). Saying such-and-such an alien species is a mammal (or, worse, a reptile, because, you know, they kind of have scaly makeup) is plain wrong. Why? Because the definition of a mammal is not the one you learnt in school. It’s not “has fur or hair, gives birth to live babies, makes breast milk”. A mammal, like any other animal, is defined not only (or even most importantly) by its physical characteristics, but by its ancestors, that is, by its evolutionary history.
A mammal is a type of animal that evolved from several predecessor mammals and proto-mammals, which evolved from therapsids, which evolved from synapsids…etc. Take a look at the figure below. This shows what it amusingly describes as the simplified descent of mammals (all the way over to the right) from amniotes (animals that have eggs which possess an amniotic membrane, namely reptiles, birds and mammals). There’s a lot there. You’ll note however that nowhere is there anything like the ancestor of Klingons. Klingons are not mammals, or amniotes, or even, really, animals.
(Figure taken from Alberts & Pickler, 2012, which you can find here)
Note too that this figure is showing the classes and clades, i.e. groupings of species. If you are looking at the evolution of one particular species, then you would need to look at each of the particular species that it descended from, thousands and thousands of them, branching out in a very complicated web of descent. For context, the diagram below details what we know of the evolution of our own species, Homo sapiens, from related hominid species.
Imagine going all the way back to a single-celled organism! The point is that the evolutionary history of any species is unique. We don’t know what life is out there in the universe. What we can say for absolute certainty is that there is only one place in the universe that you will find a mammal. And that’s Earth. Every other planet where life exists will have its own particular evolutionary process, also unique to it. If your alien looks like a mammal, walks like a mammal, talks like a mammal, and is in every way indistinguishable from a mammal, that doesn’t mean it’s a mammal. It means it’s an example of convergent evolution: similar solutions to similar problems. Live in a cold climate? Evolve an insulating structure like fur (and note that your mammal analogue (mammalogue?!) may have something that looks like fur but is made of a totally different protein. Or maybe not even a protein).
It may also be an example of a failure of imagination, of course. I don’t actually have a problem with something that is every bit like an Earth organism, as such, if it’s well-drawn as an alien: behavioural differences can be the real interest here (the Atevi of Cherryh’s Foreigner universe are a good example). I will also concede that inventing a new word for every single type of organism on a planet is going to be both tedious and non-productive, and probably confusing as well: using “tree” or “animal” as a convenient approximation, particularly as a lot of characters would probably do just that, is okay, as long as it’s clear that that is what it is.
Oh, and if you feel like pointing out that episode of Star Trek: TNG where all the funny foreheaded aliens were explained by some ancient species seeding DNA all over the galaxy? Yeh, I’m nerdy enough to know that too, and no, Klingons are still not mammals.