I haven't been in over 6 years, but I've been to Jakarta, Bali, and several other smaller towns many times. I've had very good luck getting civvies in every city I've been to. Bali at some of the hot spots has a lot of civvies and pros hanging around, tho the more upscale spots are mostly civvies and tourists.
The idea that they're muslim and super conservative...that's not my experience. The girls who are at clubs and lounges want to meet guys and possibly fuck. It's almost a self selecting group, so if they're there, they're separating themselves from the conservative crowd.
Jakarta had some extremely cool and seductive upscale clubs and lounges with very stunning civvie girls. But compared to other places in Asia, I've found the guys there to be occasionally very aggressive and territorial and we've had some tense moments with locals when chatting up local girls. Jakarta is also a very corrupt and somewhat lawless place, so if a connected local wants to fuck you up, there's zero recourse...in other words, don't push your luck, be polite, and be aware. And avoid sketchy areas...it definitely felt very sinister in some parts of town.