Some people omit the [ð], and that is common historically too, but it is quite normal (and I think more common) to pronounce the sound [ð].
That may be the case for UK English. In US English, it’s the opposite. I’ve heard it with the [ð] a small number of times, so that pronunciation does exist, but the pronunciation without is vastly more common, used in all registers, and generally not considered incorrect or substandard. And this is distinct from words like “breathes” (for example), which may undergo reduction in rapid speed but are at least pronounced with the
intention of pronouncing the [ð]. In the [ð]-less pronunciation of “clothes, there is never such an intention, so there’s nothing
to reduce. It’s simply a homophone of the verb “close.” The two sound identical; phonetically, there is
nothing at all between the vowel and the [z] — not even something that is not [ð] but not there in the verb “close.” The vowel is not lengthened, there is no constriction of any sort, etc. The tongue doesn’t do
anything it wouldn’t do for the verb “close.” The two are 100% identical in both production and perception. In the case of this particular word, deletion — not reduction — of the [ð] has produced a new, stable, consistent standard pronunciation that is acquired directly by children. Those who do pronounce the [ð] may sometimes reduce it, and it may end up sounding different from the verb “close” even if there’s no actual [ð], but that’s an entirely different process, with different outcomes, from that of those who don’t even intend to pronounce the [ð], which is the vast majority of speakers as I said.
This seems to be a clear US/UK difference.