I also posted an answer in the linked thread, though your case is slightly different.
For reference, I lived in Java and now in Bali.
It's not impossible that there are some hotels that will give you trouble, though I find it highly unlikely with neither of you actually being Indonesian.
As usual, money speaks and most places would rather make money than enforce religious traditions.
Especially in tourist locations (and I doubt you'll go that far 'off the beaten path' that I would not consider it a tourist place)
I can speak from personal experience that I did manage to rent a room with my Indonesian Muslim former girlfriend before.
I can assure you that on Bali and the Gilis you will have no trouble, extremely unlikely in Jogja too, but in some remote places in Borneo
it's possible (but still unlikely)
you'll have to try another hotel.
travel.stackexchange.com/users/28272/Sebastiaan van den Broek
You are an unmarried couple of mixed religion.
But do you have to disclose either?
The easiest solution, if neither of you has any objection to doing so , is faking both a marriage and a shared religion.
Most likely it's enough to just not disclose anything that may lead them to think otherwise.
travel.stackexchange.com/users/16546/SQB
Law says extra-marital sex is forbidden for Indonesian.
Foreigner do whatever they please.
And the mixed religion couple is no problem either.
There are many mixed religion couple in Indonesia.
They have to get married in Singapore, but this is a totally legal (and admitted) situation.
Even in Aceh
(I know Aceh quite well) you won't have any problem.
travel.stackexchange.com/users/13378/Madlozoz
Haha.
I traveled around Indonesia with a woman who was in fact my wife, but she carried a different country's passport and we certainly didn't bring a marriage license with us.
Nobody challenged us --
that may have been the wedding rings or the two small children in tow, or just the fact that hotel staff have better things to do with their time than turn away paying customers.
travel.stackexchange.com/users/405/Malvolio
I'll share my experience now that I have travelled and came back from Indonesia.
Absolutely no problem at all.
In most of the hotels, they didn't even asked about the religion.
Some did, but more in a friendly, curious way.
We always stated that we are a married couple, just in case.
We slept in hotels in Jogjakarta, Jakarta, Cemoro Lewang, Banyuwangi, Semarang, Ubud, Gili Air and Sanur.
Hope it helps somebody in the same situation.
travel.stackexchange.com/users/55127/sbyd
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 notbe 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.
travel.stackexchange.com/users/27919/motoDrizzt
I am a  muslima  with  Moroccan  passport, and my boyfriend is European. Do you think that we might have problems sharing a room in Indonesia? We do not plan on going to Aceh. We will mostly go to Yogjakarta, Borneo, Gili Islands and Bali.  What kind of trouble can we get into if any issue? Will we be just able to book separate rooms if anything occurs? Thanks!
Can a mixed-Muslim unmarried couple share hotel rooms in Indonesia?
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<legal><hotels><indonesia><religion><sex>
travel.stackexchange.com/questions/88046
travel.stackexchange.com/users/55127/sbyd
The easiest solution might be to fake a marriage and shared religion, but as you are both foreigners this will probably not be a problem. Bali would be a lot more open than other parts of the country, and you might be more likely to be refused if you booked a private guest house or apartment rather than a hotel. In general it easy to travel as an unmarried couple in Indonesia if you are travelling in tourist areas and staying in hotels. Problems may arise with individual owners on airbnb especially if one member of the couple is recognisable as a muslim. An option may be to pretend to be married.
Travelling as a mixed-religion unmarried couple is not considered a problem in the tourist areas. Foreigners basically do as they like and nobody cares. Bali is not muslim so there would be no problem there. Problems may occur with airbnb as the apartments are owned by private individuals who may object to unmarried couples, especially if the muslim person is recognisable as a muslim. Maybe pretending to be married is an option.