Parents are parents, I know, but what "current condition of general unrest in Indonesia" are you - or they - talking about?
Indonesia just completed two nationwide general elections this year, one for the legislature last April and a two-round presidential election held in July and September. Both elections were fair, peaceful, with a very good turn-out, and Indonesia now has a promising new president. I live in Indonesia, and spent most of this past summer working for the Carter Center as a long-term election observer here, travelling all over the archipelago - including places like Halmahera in Northern Maluku which were the scene of tragic large-scale violence 4-5 years ago. I never felt threatened or unsafe in the slightest. California makes me much more nervous than anyplace here.
Yes, there was an JI bomb attack on the Australian embassy in Jakarta during September. There are still at least a few JI operatives who have not been captured, and there is no guarantee that there will not be another incident. But the risk of a terrorist incident cannot be excluded anywhere in the world.
In any case, the Lembeh Straits dive ops are not likely to be very high on anyone's list. And there's no need to go through Jakarta to get to Lembeh. You can fly to Manado via Bali, or even fly direct from Singapore. If your parents were ok with your going to Kimbe in PNG last year - and there's no way to get to Kimbe without going through Port Moresby, which IS a truly scary place - then I can't imagine why they would be worried about Indonesia.
I'd keep working on them a bit longer. And you might add a live-aboard trip to Komodo or Raja Empat to the list of Indonesian options worth considering.
Frogfish