I've never heard gibberish pronounced with a hard g, but maybe I just need to travel more. As Barrie showed in his answer, both pronunciations are listed in the OED. As for the direction dichotomy, you see that sort of variant in English quite often. Pronunciation variations fall into a few different categories, such as:
- where the vowel of a word can be pronounced one of at least two ways, as in process
- where the accented syllable of a word shifts, as in redress
- where the word is pronounced differently depending the word's part of speech, as in record
(Those examples only cover officially recognized pronunciation differences, and don't account for local accents and dialects, or international differences.)
There's even an English idiom that goes:
You say tomato, I say tomato
which looks oddly nonsensical, unless you spell it phonetically:
You say təmātō, I say təmätō
The saying essentially means, "I guess we see this matter differently, but that doesn't mean one of us has to be wrong."