I never heard anyone say the “th” until I was in college. I’ve never said it that way and can’t even when I try. In case it’s a regional thing, here’s my background: Father is from SE Texas, mother is from Western PA, I was brought up in Western PA.
I can’t say as I’ve ever heard anyone pronounce the th, as such. A very slight tongue thrust changing it from “close” but no more.
I’ve just said it as naturally as possible in a number of different contexts, and I find that when it’s the last word of a sentence, I tend to pronounce the ‘th,’ otherwise not.
“I’m going to the store to buy some new cloTHes.”
“Pick your clothes up off the floor.”
Dangit, how am I supposed to know how I pronounce it naturally now that you’ve got me consciously thinking about it?
I suspect that I pronounce the TH if, and only if, I’m speaking slowly and carefully for some reason.
To the OP or anyone else who says they can’t even pronounce it that way if they try: Can you pronounce the word “clothe”? Then can you pronounce it with an S at the end?
ETA: I’m pretty sure I do pronounce the TH when I use “clothes” as a verb (e.g. “The baby’s mother clothes him warmly in the winter.”)
I voted “no”, but now think it should have been ‘other’. “Clothes” that I wear have a mostly ‘zee’ sound. “Clothes” (as in many pieces of cloth) is a ‘th’.
I say “kloze,” as does everyone I know.
I’ve occasionally heard people pronounce the “th,” but so rarely that I picked the “never” option rather than “other.”
Due to the long-ago confusion of a child relative who’s now a 30-year-old high school chemistry teacher, a single article of clothing around here is officially a “clo”. 
Just barely. It’s about as elided as a sound can be and still be there.
Yeth, thith ith me too.
I’m the same way - in fact, I wouldn’t be surprised if I think I’m saying “clothes” but it comes out “close,” the way Neil Armstrong insisted he included “a” in “That’s one small step for (a) man.”
When I’m saying something like “Close the door. I’m going to change my clothes.” I pronounce clothes the same as close - kloze (rhymes with nose). But if I’m saying something like “We’re close to that store that sells wool, linen, and other clothes.” then I pronounce close as klose (rhymes with dose) and clothes as kloths (rhymes with sloths).
The latter word is spelt “cloths”, and has a short “o”, a “th” as in “thin” and a soft “s”. “Clothes” has a long “o”, a “th” as in “those” and a hard “s” (“z”).
I’m British and it wouldn’t occur to me to drop the “th” sound in “clothes”. If I did then I’d be saying “close”.
Edit: and to Little Nemo. Is the word “cloths” (as in “more than one cloth”) really spelt “clothes” in the US?
I’m from the UK, and I always pronounce the th in clothes - like Colophon, it would never have occurred to me not to. Maybe it’s a US/UK difference - does it vary around the US?
This.
Not that I know of, which is why I found Folacin’s and Little Nemo’s posts confusing!
I do pronounce close and clothes slightly differently, but they would sound somewhat similar. I think if you recorded me and listened carefully, you’d at least noticed a longer pause on the z-like sound as I try to fit a th and a z in next to each other. But you won’t hear a nicely delineated th sound like you would if I was saying cloth. th and z just don’t go together like th and s do.
So, for poll options, I did answer that I pronounce them differently but I’m willing to admit that it’s a different that might not be obvious to a casual listener.
As a ‘z’.
“Cloze” The ‘h’ iz silent.
So… for the people who don’t pronounce it: do think of it as incorrect, when you reflect on it?
Like, in the UK there would be a fair number of people who would say “cloves”, but really everyone knows it’s wrong. Even though plenty of people do it and among certain people it would never be commented on, you still know it’s wrong.
Is that how they call “hard” vs “soft” s on your side of the Pond? I’ve always known “soft s” as the Z sound (as in “as in close/kloze the door”) and “hard s” as the sssssss sound (as in “sound of slamming” the door).
(And yes, multiple pieces of cloth would be “cloths” and pronounced with hard “th” and hard “s” (that is, like sloths, as I understand the usage of “hard” and “soft”)).
Who here pronounces the “ph” in phthalein or phenolphthalein? How is it 'sposed to be pronounced? (Me: ISTM I’ve seen it described as either silent, or pronounced like f’thaleen, which sounds like something the acolytes of Cthulhu would say. Depending, of course, I suppose, on how you pronounce Cthulhu )
Who here pronounces the second “e” in vegetable? (Me: Usually “VEJtabul”)
Who here pronounces the first “d” and/or the second “e” in Wednesday? (Me: Usually WENZday.)
+1
I just started adding it only recently. I don’t know why, except I’ve noticed audio book narrators usually do pronounce the* th*. I guess it helps a tiny bit because then it’s no longer a homonym with close, which maybe could cause confusion very occasionally.