Divorce seems remarkably casual in ancient Rome.

Marriage required the consent of both partners at the beginning and throughout the relationship (Dixon, p. 81). Should one partner withdraw consent, the marriage was ended. Roman law did demand that "grounds" be given for divorce (Twelve Tables 6.10), the two most common being adultery and infertility. This requirement, however, was very flexible. Valerius Maximus describes how a husband divorced his wife for adultery simply because she went into public with her head uncovered (Facta et dicta mem. 6.3.10).

Is this because we have a primarily aristocratic view on the subject?

Probably. Marriage was a political relationship for the aristocracy, as frequently and as easily dissolved as any political alliance. It was likely different for those outside the aristocracy, who had markedly different aspirations. Our sources don't say much about them, however.

Were women as empowered to initiate proceedings as men?

Yes and no. It was harder -- though not impossible -- for a woman to divorce her husband for adultery. Since she brought a dowry to the marriage, there were also complex financial considerations that made divorce more difficult: Can she demand the return of her dowry? What if her husband has already spent the money? etc. However, it was increasingly common for a woman to remain in the power of her father upon marriage. In this case, divorce was an arrangement between men (though the woman could object).

Could they expect to emerge financially and socially intact, or did Rome share other societies stigma for experience women?

As to remarriage: Since marriage was often primarily a political relationship, a father-in-law's power mattered more than his daughter's sexual history. Socially, there are indications, especially in our late Republican sources, that divorce could sometimes be considered a scandal. It was less the fact of divorce, however, and more the reasons for the divorce. Financially, as mentioned, the disposition of the dowry could be very tricky. Most of Roman law on divorce deals more with these financial considerations than with justifications for divorce. Also, custody was usually awarded to the father.

See especially Susan Treggiari, Roman Marriage (1993). It's the go-to source on Roman divorce. Also Suzanne Dixon, The Roman Family (1992); and for the law, Judith Evans Grubbs, Women and the Law in the Roman Empire (2002). NB: Things changed somewhat in the fourth century. See Geoffrey Nathan, The Family in Late Antiquity.

Ok, so first thing to bring up is that I am on vacation and do not have my research materials on me at the moment so I cannot give you exact answers. But if this is something you a curious about, I would urge you to check out Eve D’ Ambra’s Roman Women as a good overview on the subject.

Though it would be super interesting to know what roman marriage was like, we only have small vignettes of what life was like back then and we often have to be critical of the reliability of the information that has been passed down to us. You are absolutely correct we see an aristocratic view of Roman marriage and this heavily influenced how we understand it.

Divorce was never a good thing, for the man or the woman. It was seen as a mark of failure for both parties unless there was a political element involved. It was not uncommon for a man to set aside his wife to marry a political ally’s daughter, niece, etc. However if there was just something wrong with the marriage it didn’t look good on the man because, in theory, he should be in complete control of his household. The woman took most of the blame for the failure of a marriage. If a woman was divorced it could be because she is barren or she did not complete her matronly duties in a satisfying manner.

Divorce, imho on the matter, would not have been a very empowering experience. After a divorce, a woman would loose, what we would consider, custody of her children. They would legally no longer be her children. See Jane F. Gardner’s Women in Roman Law and Society for more information on family authority of the paterfamilias.

As far as remaining financially intact, it’s kind of hard to explain but to put it in simple terms she was property. Her husband would be giving her family’s property back to them and that would include her and her dowery. After the divorce she would, in a manner of speaking, belong to the head of her household. Remaining socially intact? No, not really. When sources tell us about women (and even men) having multiple divorces it is not considered an acceptable thing. It is something a political rival will use as proof against your character.

In short, it was very much a stigma then and the roman ideal was to have a marriage last until death and you would care for each other as companions who each had tasks to complete in order to keep the household intact. Passion and affection was not required or even expected. Cato the younger, who considered himself a torchbearer of Roman identity, mentions that he only held his wife when it stormed outside to comfort her.

What time period are you referring to in this question? The Western Empire lasted from 753 BCE to 476 CE. The treatment and social statice of women changed dramatically during certain periods of the Empire.