Church clergy tend to be elites and educated. I'm not sure if evidence exists out there, but is there anything that tells us whether key members in the Vatican actually personally rejected these scientific claims, or was it just a ploy to maintain Church power (i.e. they believed the science, but pretended to reject it)?
Well to begin with, the Catholic Church never had an official stance on evolutionary theory until the mid-20th century (when it said that it was fine). Certainly, you could find priests who opposed it, priests who didn't care, or priests who actually contributed in some way (Mendel's development of genetics being a tangential example- Genetics can stand on its own but is also important to evolution, obviously).
As for Galileo, the issue is more complicated than commonly related. First of all, Galileo was already a well respected, famous scientist for his work on physics, but that didn't make him perfect. Heliocentrism was at Galileo's time a fringe theory, which most of the scientific "community" (though such a thing was only developing at that time) rejected. Galileo hardly had proof for his ideas, and was indeed stumped when questioned about the apparant lack of stellar parallax, which should exist according to Heliocentric theory (we now know, of course, it is simply too small to be seen normally, but at that time, it seemed to be quite the glaring hole in Heliocentric theory). Finally, Galileo was a rather egotistical, abrasive man. He considered opponents to his yet-unproven hypothesis idiots and simpletons. He was also originally allowed to publish his work, but got into big trouble when said work pretty much called the Pope a "simpleton". Galileo's rivals used this as an excuse to bring him to trial. Galileo was rather aggressive and arrogant and this certainly didn't help his case. He was found guilty and placed under a very loose house arrest.
Despite this, Helicentric theory initially caused little uproar in the Catholic Church. Copernicus's works were generally left alone in the official sense, but we're heavily bashed by scientists and theologians at the time.
So to answer your question: yes and no to Darwin, but they did not accept Galileo's theory, though again, this was actually in agreement with most of the scientific community at that time.
My source for most of the Galileo info is chapter 6 of History's Greatest Lies by William Weir.
Not Catholic, but according to Jeffery Moran's The Scopes Trial: A Brief History With Documents, there was little conflict between accepted American theological thought and the Darwinian scientific thought prior to WWI. Many Christians simply took the meaning of the word "day" to be symbolic, not literal. The class between science and religion in America didn't begin until the 1910s and 1920s, when changing social norms forced people with conservative views to react by joining the loud ultra conservative minority (not unlike Republicans with the Tea Party). Unfortunately, this schism grew to the point where creationism and Darwinism became almost antithetic, thus culminating in the infamous Scopes Monkey trial.
Most of the religious pushback to Darwin in his own time was within England. Most people in continental Europe didn't really care. Darwin's theories weren't really new -- his own grandfather Erasmus had been arguing versions of them when Charles was a child. In England the church was bound up with notions of civil propriety (read: they were more staunchly middle class than other churches elsewhere), and so they had to argue about it publicly.
Galileo successfully convinced the Church that the phases of Venus implied that a simple Ptolemaic model could not work. They instead adopted a Tychonic model, which is indistinguishable, experimentally, from the Copernican model. So he did convince them of something! Just not his philosophical interpretations of the data. See Kuhn, The Copernican Revolution.