Staying togather without marraige ..Illegal??

Its OK with me but it depends where they live but I would suspect there would be no issue if not Indonesian. Religion doesn't enter it if not from Indonesia really.

Unless you're in Aceh, it won't be a problem anywhere in Indonesia. If you're respectful, pay your bills and are "good neighbors" you won't attract any attention other than you are foreigners which the locals will be curious and friendly. Aceh has stricter requirements on all residents under their religious regulations which include co-habitation, riding together on scooters, public displays of attention and dress codes.

I understand it's strictly illegal but commonly ignored. I knew of one English bloke who was told to move out by  the cops but the local lady in question wasn't officially divorced at that time so there were obvious complications.
I also know of one cop who was considering if a local and a foreigner were married when he saw them book into a hotel with a view to doing something about it.
Other than that, the big deal (if any) is going to be the local village head and their opinion of unmarried couples. If they don't like it, they can block any and all official paperwork so leave you without SKTT or KTP, thus you aren't 100% legal in Indonesia so liable to arrest. It would also naff your chances of driving licences and so on if they blocked you.
Complaints from the local community might also cause that but any such problems seem very rare.

At the time I was not married yet to my Indonesian wife, and even that she is not muslim, we choosed to rent 2 different rooms in the same kost until we got married. It's more about tradition and to avoid gossips behind us. After legally married we only kept one room.