It’s quite common to distinguish the pronunciations of "golf" and "gulf". Historically, they had the different vowels that the spelling would suggest: a “short o” ("lot") sound in golf and a “short u” ("strut") sound in gulf. In American English, the “short o” sound has typically been rounded to the “cloth” vowel when it comes before /l/ followed by another consonant (or followed by the end of a word).
According to Wikipedia, a general merger of /ʌl/ and /ɔːl/ (“strut” + l and “cloth~thought” + l, as in "hull" and "hall") is known to occur in some accents of American English, but it is not a mandatory feature of “standard” pronunciation and I don’t think it’s very common. I've heard of speakers having the merged vowel be /ɔ/, in which case this could be seen as a kind of rounding change, maybe similar to the one that produced /ɔl/ from what would have otherwise been /ɑl/.
For me, in the specific context of a following voiceless obstruent (which causes the preceding syllable nucleus to become shortened or "clipped"), "strut" + l does sound somewhat confusable with "lot~cloth~thought" + l, but not to the extent that I would say that I have a merger. For context, I have the lot-cloth merger, so phonemically I have /ɑlf/ in "golf" and /ʌlf/ in "gulf". It seems plausible that some speakers with accents similar to mine might have something like "Canadian raising" here that turns former /ɑlf/ into something that sounds more like /ʌlf/, just as /aɪf/ in words like "wife" is turned into [ʌɪf]. There was a post on ELU relatively recently by a speaker who perceived /ʌ/ rather than /ɑ/ in the word "scarf" (but not in "scarves"), which seems similar.