I think it may make some sense to provide a bit of cultural background to shed some light on this movie, and help people decode it better.
As some other viewers already pointed out, the plot is based on a true story. Romanian media ran the story some years ago dubbing it a case of exorcism gone bad. A priest supposedly mistook a form of mental illness for satanic possession, the exorcism performed on the respective nun leading to her death by starvation. In reality, the nun was no such thing, but just a girl visiting the convent. The priest and the other nuns, who after a previous seizure had already referred the woman to a mental hospital, were talked into taking her back after she was discharged. Back at the monastery, the girl had another fit of sorts and they had to restrain her. A few days later she was dead from exhaustion. The court trying the case found the priest and some of the nuns guilty of wrongful death. The entire case was brilliantly documented by former BBC-journalist Tatiana Niculescu-Bran in two books, which the screenplay was based upon.
The affair did raise some questions regarding Romanian society, Cristian Mungiu was able to only shed a brief light on those aspects, but I think they are crucially for understanding the context.
The priest was somewhat of a maverick in the church. Mungiu implies that by telling that the Bishop would not bless the church, although it is more popular than the churches in the valley, and by having one of the nuns explaining that he has fallen in disgrace after renouncing his pay (Romanian priests are payed by the state). The Romanian region of Moldova is the poorest in the entire European Union, but - and probably for this exact reason - also a religious hotspot. In stark contrast to the poverty stricken people, the Romanian Orthodox Church is one of the richest entities, operating in such lucrative industries like timber, tourism, and manufacturing of religious paraphernalia. Clerics are supposed to be part of the game, when they refuse to do so, they basically get sacked - or, as in the present case, go rogue, retreating to makeshift compounds and recruiting "true" believers. On the other hand, people disappointed by the church's obsession with money tend to be attracted to such rebel priests, seen as more mystical and in line with the biblical way. The fact that the priest was an outcast prevented the church to openly take his side, although they pretty much come to the help of (morally) corrupt men of the cloth. People of a more secular background frown on both kinds of clerics, viewing them as blood sucking opportunists who prey on helpless, naive people. That explains the outburst of the doctor who receives the lifeless body of Alina towards the end of the movie, but also the implication of the foster father of sorts, that the nuns tried to rip her off by charging her more for medication expenses.
The relationship between the two girls is psychologically complex. Mungiu leaves some clues for a past love affair, but refrains from being explicit on the matter. The fact that the girls obviously love each other may have a different explanation. Like many other children, they grew up in an orphanage, being abandoned by the poor parents in the last years of the communist regime. Mungiu suggests multiple abuse in the facility and foster families, which we know to massively have occurred in those care homes. Alina came to be the protector of Voichita, who is a perfect victim. She would defend her fiercely and sees her new found "family" as a threat. Being possessive, it is possible that Alinas reaction is based on a jealousy, but she is also ambitious and may experience a sense of failure and guilt - she went abroad, leaving the gullible Voichita at the mercy of the manipulative priest, and now that she wants to take her back, Voichita seems to be firmly controlled by him. So Alina is in a threefold predicament: the backward priest sees her as a threat because she has been infected with Western sins and does not fit in his way of life, threatening his influence on the compound; she fails in convincing Voichita to join her; she has no place to go, having lost her job on a cruise ship in Germany. That could be enough to break a person and send her into despair.
Having said that, because at least Romanian viewers generally know the story and the backdrop, they are left only to pass judgement on the way Mungiu told it. In my view he does a good job.