It has no pace, sloppy continuity, zero humor, bland characers on top of being totally devoid of either warmth or humanity.

-- Starlog magazine, September 1982 issue, E.T. on the cover

If you ask John Carpenter himself about why The Thing did badly amongst critics and audiences at the time of its theatrical release, he lays everything at the feet of E.T., the Spielberg movie about an alien who wants to phone home. Here's Carpenter himself from a 1999 interview:

Two weeks before our movie comes out, they release this other movie called E.T. And there's this burst of love all around this movie. I guess the country was going through a recession and there were tough times ... Two weeks later, out comes my movie. And my movie is exactly just the opposite of E.T ... It is a downer. It is the grimmest thing you have ever seen. Here I thought I had made this really great movie, right?

I think this possibly could have some audience effect, but note the rankings of movies 1-8 on the weekend The Thing was released:

E.T., Blade Runner, Firefox, Rocky III, Star Trek II: The Wrath of Khan, Annie, Poltergeist, The Thing

Ahead of The Thing we have three sci-fi classics (E.T., Blade Runner, Wrath of Khan) and one horror classic (Poltergeist). Blade Runner was released the same weekend as The Thing. So it was fighting against a stacked deck -- I don't think we can read too much into the eventual ~$20 million in box office (it was made for $15 million).

Also, the presence of Blade Runner indicates to me that a summer-of-82 movie could be successful (*) without rainbows and unicorns (a unicorn did make it into Blade Runner, but not the theatrical release). So I'm skeptical about the mood of the country somehow requiring an E.T. outlook.

Poltergeist did get a much warmer initial reception, so maybe the best thing to do is just to compare reviews. The same person at the New York Times (Vincent Canby) reviewed both of them.

Poltergeist:

More important are the film's extraordinary technical effects, by which we are made to see and experience the terrible assaults these angry spirits make on the Freelings, sometimes occupying their minds as well as their house. These effects are often eerie and beautiful but also occasionally vividly gruesome.

The Thing:

It's entertaining only if one's needs are met by such sights as those of a head walking around on spiderlike legs; autopsies on dogs and humans in which the innards explode to take on other, not easily identifiable forms; hand severings, immolations, wormlike tentacles that emerge from the mouth of a severed head, or two or more burned bodies fused together to look like spareribs covered with barbecue sauce.

So Poltergeist has "eerie and beautiful" effects that are "occasionally vividly gruesome" while The Thing has a list of body horrors. I think this is the actual key to the difference in reception.

While there were plenty of movies with an equal or even higher level of violent content they weren't really mainstream releases; The Thing, on the other hand, was Carpenter's big break with Universal.

So The Thing's intense cavalcade of gruesome transformations and deaths was far above what some of the critics would have previously experienced. Carpenter from a 1985 interview with Starlog:

I was called 'a pornographer of violence.' I had no idea it would be received that way ... The Thing was just too strong for that time. I knew it was going to be strong, but I didn't think it would be too strong ...

I think the reviewer exception here would be Roger Ebert, who clearly had more familiarity with such movies and calls it a "a great barf-bag movie", giving it 2.5 stars (Poltergeist got 3 stars). He also goes on to say

... he has populated his ice station with people whose primary purpose in life is to get jumped on from behind. The few scenes that develop characterizations are overwhelmed by the scenes in which the men are just setups for an attack by the Thing.

The characterization is almost universally panned in every 1982 review.

And the other reason I think critic reception might have been frosty is... as far as individual characters go, are they wrong? The Thing, in a way, is not composed of characters, it is composed of a crew, it is composed of humanity itself, and the fear and emotions that come when humanity cannot trust itself. It is operating on a different expectation level than following the development of characters (even though it certainly has them and you can follow their development -- but it's easier on re-viewing). It is intentionally paranoid and confusing.

In retrospect, not all art needs to be designed the same way; not every painting needs to represent realism, not every piece of poetry needs rhyme. The Thing almost needs understanding on a meta-level with a different metric, so it is understandable that critics of 1982 differed in their prose.

Back in 1997 Carpenter told Empire that "You'll never, ever, see anything like The Thing again." Like MacReady and Childs we're still waiting. We might be for a long time yet.

-- From a review in 2000, via Empire

...

(*) Blade Runner overall box office underperformed, but it had two strong weeks to start and suffered from the same crowded schedule.

Muir, John Kenneth. The Films of John Carpenter. United States: McFarland, Incorporated, Publishers, 2015.

I would like to add- not as an answer but as additional information that could help others form answer- that John Carpenter’s The Thing is not the original. The Thing From Another World(1951) was the first iteration of this creature, name, and narrative. The Thing(1951) is suggestive of its era.

Scientists uncover a crashed and frozen UFO, and decide to take it back to their Antarctic base for possible study. A heating device is left on, accidentally thawing and releasing the creature.

In many ways, The Thing reflects, and even predates the other giants of its genre at the time, Gojira(1954), Them!(1954), The Beast from 20,000 Fathoms(1953) and many others. All of these could fall under the human ignorance and meddling with things not to be meddled with ideas. I have already spoken about the historical, theatrical, and cultural significance of Godzilla, and would gladly for many thousands of words. It is by far the most complex of many of the listed, it will not be discussed here.

The Thing(1951) shows how scientific and human intervention and ignorance in things not needing to be meddled with can cause disastrous consequences. Similar to the others, the Thing itself is an advanced plant-like life form, of which I have for years called “The Vegetable.” It was typical and almost cliche for its era, yet it also included horror-esq. elements that were somewhat new to the genre. It was baseline, not over the top, not horrible, a decently entertaining, if sometimes slow, watch.

Roger Ebert wrote that some thought that there were anti-communist messaging, which is not impossible to see this perspective. The fear of an outsider, an “alien” was a very real fear during the 1950s, especially with McCarthyism making the rounds.

My guess is, as movies evolved and the horror genre fleshed out during the 70s, and 80’s, monsters and practical effects were considered tacky and outdated, not suitable with then modern horror scene. Characters like Freddy and Jason were ruling the genre, and the macho era of monster killing in the 1950’s and 60s had died out.