Well, enough crazy-talk... It's obviously a matter of english phonotactics. You know, traditionally /g/ comes in two flavours, hard and soft, or rather it bears both front and back allophones realized according to the phoneme’s environment... But, come to think of it, the more one explores the situation the more it should seem that [gɪf] is quite - if not totally - unnatural, as it's not a fully fledged word yet...
Indeed, [gɪf] is a neologism, borne of an acronym which itself isn't spelled [gɪ.aɪ.ɛf] but rather [d͡ʒi.aɪ.ɛf], as supposed by the rules of spelling, regardless of the allophone of /g/ realized in the original first word of the acronym. And yet, should the word be pronounced in a way that must concur with that realization, even if the spelling of the acronym itself doesn't? Why? Just to forcibly - and with total lack of elegance and respect for english phonology - elucidate us on a purely etymological matter? Shouldn't a word be one of its own right, yet belonging to the rest of the english corpus? And when it comes to our primal urge of asking “why”, shouldn’t we let etymology play it's role, after all? Substance versus Form! Not to mention, Deviation versus Conformity!
In any case, when it comes to a purely linguistic argument, I subscribe to the idea that [d͡ʒif] is even more valid than [gɪf], if anything, since it’s the final outcome of the transcendence of an acronym to the realm of actual words - yet not necessarily of platonic forms - and not some fuzzy step somewhere in the middle of the road... There is of course a limited set of words of germanic origin where /g/ is realized as [g] even when preceding front vowels, like /i/, or /e/, as in [gɪv] or [get], but I’m not sure if the specific process that made people retain consonantal backness immidiately before vocalic frontness is still ongoing. In fact, I suspect it isn’t, or at least it’s recessive, lest we would have many more such examples.
So, after all, why assigning a neologism to a set of words that have seemingly become an exception to the rule - perhaps, in part even due to their great old age? Mixing a fledgling with fossils and calling it a day? Sloppy botchers! To me, [d͡ʒif] is more of a word than [gɪf] could ever be! And of course, I pronounce it like so!