The words next-door neighbour and postdoc are nearly always said without a 't'. The Oxford Dictionary online gives the transcription as /pəʊs(t)ˈdɒk/, and the audio clearly says the word without a /t/ sound. You can listen here.
Where does this /t/ go to and why is it allowed to disappear? I looked at the top-rated answer answer to this question here: Why is "cupboard" pronounced with a silent "p"?
That answer states that it is because the 't' and the 'd' in postdoc and next-door neighbour are the same apart from that t is voiceless and d isn't. When two consonants are made in the same way in the same part of the mouth like this, then one of them can disappear. That's what it says. But, I double checked with some other English Language scholars and they say that this isn't true at all.
They point out lots of examples where the 't' usually disappears but the next consonant isn't a /d/, isn't made in the same place, and isn't the same type of consonant. For example guest book is normally pronounced guess book. Here are some more:
- left me
- kept calm
They also pointed out the following where we get a /dt/ or /td/ sequence, but neither the /d/ nor the /t/ can be missed out.
- bedtime [*bed ime]
- head teacher [*head eacher]
- feet don't hurt [*fee don't hurt]
- meltdown [*meldown]
What's going on? Is there a phonological rule here? And where have all those /t/s gone?