Well, "Indonesia" is a big word. And a big world by itself.
First of all, it all comes to who is the subject: Muslim law has nothing to say over kafir, it's (mostly) their own problem what they do with their lives. So, when it's about touristic areas or hotels for tourists, you are mostly free to do whatever you want.
This does not apply, anyway, to privately owned places; in short, if you book a guest house or an apartment, or things like AirBnB...the owner has all the rights to prohibit your staying once he discovers that you are an unmarried couple; I've seen myself this in a couple of place in Indonesia, there were signs stating it.
But keep in mind that all of this depends on the island, too, and the area:
- Bali is out of question, it is the only big Indonesian island to not
be Muslim, so they never make troubles there.
- Gili is another touristic destination, so they'll just ignore mostly everything
- Jawa can be complicate depending on the area. Basically it's mostly Muslim, but there are part of Jawa which are more free and some which are more strict. But again, if you limit yourself to normal hotels nobody will ever have something to say. Maybe in rural areas do not kiss in public, but Yogja is hardly rural :-) (while I hade my share of shivers, I must admit it, in Lumajang)
Final point is, obviously, if you are recognizable as a Muslim. That the case, it can become very complicate even in a normal hotel as someone can get offended by your lack of respect for the tradition (not me, ok? Just saying, not implying anything), but as a Muslim yourself you already know it, and anyway you wrote in comments that you are not recognizable as such.