Wikipedia is pretty accurate. When I was learning, I had no idea what was going on linguistically so I just learned on a case-by-case basis. Suki, desu and shukufuku sounded like ski, dess and shkufku. Uta, fuku and getsu kept their /ɯᵝ/ (which I didn't know wasn't a /u/ but knew was kind of funky) for the most part. I occasionally heard it disappear in words like getsu, though that was typically by males or in very casual speech.
As Wikipedia points out, people trying to sound super formal/feminine, keep the /ɯᵝ/ and even emphasize it.