So as far as I understand, or what is commonly understood, is that part of the reasons Jews were well off in Europe during much of history is because Christians were not allowed to lend money to other Christians, where the Jews inserted themselves as money lenders. My question is how did we reach the point where nowadays it's common for anybody to be part of the banking/lending profession?
Your question isn't necessarily a bad one, but it's assumptive.
Christians have always been bankers. Christian banks were a way for people to keep stores of precious metals safe and in so doing, the receipts the bakers gave their customers were used as notes of exchange. Bankers grew wise to this and started making notes on reserves they did not have. This is the beginning of fractional reserve banking.
Now, thinkers as early as Aristotle condemned usury, and Thomas Aquinas was chief among this condemnation in the middle ages. As the middle ages grew, and commerce expanded, bankers developed a way to profit from the trading of notes of exchange: a very rudimentary foreign exchange market. This totally circumvented usury laws at the time since money was not being lent, but changed into another currency for use in another country to buy goods and services (cloth, soldiers, etc.).
The Catholic Church had little it could do as it was financing it's own business endeavours (ie mercenaries) and saw its adversaries effectually cornering the market to suit their needs, making the currency the church was using devalued. When was it allowed? It's never been allowed, but penalties were lessened and violations "overlooked" when necessary.
Naturally it's must easier to get the money you need by borrowing and not by working the exchange get market. The Church needed money quick and saw its usury law as a barrier to survival in Europe.
I would like to clarify a few points that were made here.
/u/rocksteadymachine is correct in the fact that Christians have always been involved in the storage of money, or more generally, wealth. Even before the Christianity was "legalized" (an imprecise term in this case) by the so-called Edict of Milan (it was neither a true Roman edict nor was it actually issued from Milan) the Church(es) of the late Roman Empire organized and facilitated the storage and transfer of wealth as indicated by the letters of St. Cyprian. I'm sure better evidence of the capacity exists, but I'm at least familiar with the corpus of St. Cyprian.
Again, /u/rocksteadymachine is correct in that "banking" got its start as primarily a profession of moneylenders. A banco literally refers to a/the counter behind which a money changer sat and changed currencies, or goods for currencies. Perhaps the most well known example of this is the Champagne Fairs where Italians facilitated the exchange of currency. During this early period, a bancarius was an individual who knew the value of coins in circulation and checked the quality of coins in circulation. The Genoese were the first Europeans to introduce the idea of deposit and reimbursement on demand.
The core of OP's question concerns the prohibition of usury in the Middle Ages. Thomas Aquinas wasn't pulling this prohibition out of his ass. Indeed, Thomas was hardly innovative when it came to his theology. He was essentially a compiler and elucidator (is that a word?) of very orthodox theology. Leo I (401-474) essentially said that lending at interest was the death of the soul(!). Leo is hardly the first major Christian figure to ban lending at interest, but he's an important figure nonetheless. I'm not trying to downplay what Thomas did, his Summa is a work of staggering intellect and scholarship. For Thomas's reasoning see, Summa theologiae, IIa IIae, q. 88, a. 1, Resp.
The ban imposed on usury has a solid scriptural basis. See Deuteronomy 23:21-22: "You shall not charge interest to your countrymen: interest on money, food, or anything that may be loaned at interest. You may charge interest to a foreigner, but to your countrymen you shall not charge interest, so that the LORD your God may bless you in all that you undertake in the land which you are about to enter to possess."
There are other examples of the prohibitions of usury in the OT, but this is one of the most clear cut examples. The Hebrew people were not unique in their time for banning usury. I think they understood the strife that compounded debt causes. That said, it was the Hebrew scriptures that concerned the Latin Christians of the Middle Ages. Medieval scholastics turned to Aristotle for an explanation of why lending at interest was bad. He essentially said that money was an inanimate object and interest is essentially an inanimate object reproducing, which goes against nature.
I would contest the idea that medieval lenders knew what they were doing was sinful. I use the term lender because medieval Italians always believed usury to be a sin and would not participate. That said, they were very good at finding loopholes. They would, however, accept that they were operating in a theological gray area and perhaps pushing the bounds of theological decency.
As /u/rocksteadymachine rightly points out, the exchange of currency (cambium per litteras) was the earliest loophole. Although interest was obviously concealed in the exchange, such an exchange could be passed of as a mutuum (a loan without interest in Roman law, a legal transaction in both the Old and New Testaments).
By the second half of the 13th century Henry of Susa suggested that money lent constituted a loss of gain. I.e. an individual did not have the ability to pursue profit with his money if it was being used by another individual, and thus could be compensated for that. By the 14th century, state and Church institutions began to simply back off of usury and let the earlier justifications stand. Indeed, by the second half of the 15th century, the Franciscans had developed the concept of the Monte di Pieta or an institution that granted free mutual credit. The Monte dei Paschi di Siena is the oldest still operating bank in the world (http://english.mps.it/) started out as a monte di pieta.
(Source: Oxford Encyclopedia of the Middle Ages, de Roover's still useful explication of medieval banking in The Rise and Decline of the Medici Bank, and I'm sorry about the vagueness of this citation, but general knowledge gained as a Ph.D. student in medieval Italian economic history).
Edit: Minor source issue.
From what I remember of my art history degree, just because Christians say usury is frowned upon, doesn't mean people won't do it anyway. One name you might recognise is the Medici family from Florence, who made their fortune in banking. Others included people like Reginaldo Scrovegni and Chancellor Rolin, who both made their fortunes in banking.
One of the central ideas to the Catholic church was penitence, where you basically pay for your sins (usury) in a way that your church deems acceptable. For the people mentioned above, sure, they sinned, but they atoned for their sins by patronising and/or donating art (or, in the case of the Medici and Scrovegni, entire chapels), so they can secure their (families') spots among the Blessed come Judgment Day.
Take the Arena Chapel, for example. Imgur Imgur You see Giotto's Last Judgment fresco where, on the bottom center-left, Enrico Scrovegni is literally presenting the chapel to the Archangel Michael, the Virgin of Annunciation, and the Virgin of Charity (who holds out her hand to Enrico in acceptance). Symbolism in the fresco abound, basically it shows that the saints have accepted Enrico's penitence for his father's sin of usury, and they'll still be welcome in heaven when the time comes.
That's the kind of pattern you get in a lot of altarpieces (e.g. Van der Weyden's Last Judgment exterior), devotional paintings (e.g. Van Eyck's Rolin Madonna), etc. where you get the people who have sinned repenting by commissioning these pieces, and then they depict themselves as being introduced to saints or baby Jesus or whatever by their patron saints, or someone relevant, in order to absolve their sins.
I've rambled on for enough already, but from my understanding, it's not that they didn't sin/lend money, it's just that they have ways of making sure they still got into heaven regardless (which is really their ultimate concern).