WikiPedia on that subject quotes this article, which alleges that Catholic teaching accepts but doesn't require the theory of evolution.
Or a more authoritative answer about Catholic teaching is for example this from Pope Benedict in 2007, quoted on the Vatican web site as follows:
Currently, I see in Germany, but also in the United States, a somewhat fierce debate raging between so-called "creationism" and evolutionism, presented as though they were mutually exclusive alternatives: those who believe in the Creator would not be able to conceive of evolution, and those who instead support evolution would have to exclude God. This antithesis is absurd because, on the one hand, there are so many scientific proofs in favour of evolution which appears to be a reality we can see and which enriches our knowledge of life and being as such. But on the other, the doctrine of evolution does not answer every query, especially the great philosophical question: where does everything come from? And how did everything start which ultimately led to man?
Another example is at In Creation God Calls the World into Existence from Nothingness by John Paul II in 1986, which reads like a sermon about Genesis. In it, the Pope says,
Above all, this text has a religious and theological importance. It doesn't contain significant elements from the point of view of the natural sciences. Research on the origin and development of the individual species in nature does not find in this description any definitive norm or positive contributions of substantial interest. Indeed, the theory of natural evolution, understood in a sense that does not exclude divine causality, is not in principle opposed to the truth about the creation of the visible world, as presented in the Book of Genesis.
I interpret this as saying that the Book of Genesis is a product of its time and is not scientific, and that the theory of natural evolution is not incompatible with Catholic theology.
The same goes on to list the various things which (unlike evolution) are important articles of faith, for example:
1) The one, true God is Creator and Lord "of visible and invisible
things" (DS 3021).
2) It is contrary to faith to affirm that only matter exists
(materialism) (DS 3022).
3) It is contrary to faith to assert that God is essentially
identified with the world (pantheism) (DS 3023).
4) It is contrary to faith to maintain that creatures, even spiritual
ones, are an emanation of the divine substance, or to affirm that the
divine Being by its manifestation or evolution becomes everything (DS
5) Also contrary to faith is the idea that God is the universal or
indefinite being which in becoming determinate constitutes the
universe divided into genera, species and individuals (DS 3024).
6) It is likewise contrary to faith to deny that the world and all
things contained in it, whether spiritual or material, in their entire
substance have been created by God out of nothing (DS 3025).
I found it interesting to compare Benedict's statement quoted above, with the following paragraph from Humanis Generis from Pope Pius XII in 1950 (emphases are mine):
[36.] For these reasons the Teaching Authority of the Church does not forbid that, in conformity with the present state of human sciences and sacred theology, research and discussions, on the part of men experienced in both fields, take place with regard to the doctrine of evolution, in as far as it inquires into the origin of the human body as coming from pre-existent and living matter - for the Catholic faith obliges us to hold that souls are immediately created by God. However, this must be done in such a way that the reasons for both opinions, that is, those favorable and those unfavorable to evolution, be weighed and judged with the necessary seriousness, moderation and measure, and provided that all are prepared to submit to the judgment of the Church, to whom Christ has given the mission of interpreting authentically the Sacred Scriptures and of defending the dogmas of faith. Some however, rashly transgress this liberty of discussion, when they act as if the origin of the human body from pre-existing and living matter were already completely certain and proved by the facts which have been discovered up to now and by reasoning on those facts, and as if there were nothing in the sources of divine revelation which demands the greatest moderation and caution in this question.
Compared with Pius, who 'doesn't forbid men who are experienced in human sciences and theology to research and discuss evolution, both for and against, while submitting to the judgement of the Church which has the Christ-given mission to interpret Scripture and defend dogmas of faith', Benedict seems more sure that there's some merit to the theory of evolution, when he opined, 'the antithesis [between believing in God the Creator and believing in evolution] is absurd because, on the one hand, there are so many scientific proofs in favour of evolution which appears to be a reality we can see and which enriches our knowledge of life and being as such'.
IIRC Benedict had a reputation for being well-versed in and supportive of the traditional Church doctrines; so I infer that Benedict's view is the result of the 57 years-worth of "opinions, favorable and unfavorable to evolution, weighed and judged with the necessary seriousness", to quote Pius.
Replying to a comment below,
What I'm missing from the answer is the church's stance on creationism. Is it correct to say that the "literal" interpretation of the bible, and specifically the book of genesis, is not accepted by the catholic church?
I can't define "creationism", but the Catholic Church's teachings include more than a merely "literal" interpretation of the Bible: for example, there's the historical text (different languages and versions); the literal meaning of the text; and the spiritual meaning of the text. Some of it is "allegorical". The Church would want people to understand it with what may casually be called 'a grain of salt', or more formally, "the Holy Spirit", as well as the "Magisterium".
I wouldn't extract quotes from the following references, because quoting sentences and phrases out of context might not give a true view of Catholic teaching; but if you want to see how well I paraphrased it in my previous paragraph above, I invite you to read:
I don't believe that the Pope's comments in a meeting are considered authoritative decision on Catholic doctrine, just an opinion. Compare that to an Encyclical like "Humani Generis"
Wikipedia's article on "Encyclical" in fact quotes from Humani Generis, which says:
[19.] Although these things seem well said, still they are not free form error. It is true that Popes generally leave theologians free in those matters which are disputed in various ways by men of very high authority in this field; but history teaches that many matters that formerly were open to discussion, no longer now admit of discussion.
[20.] Nor must it be thought that what is expounded in Encyclical Letters does not of itself demand consent, since in writing such Letters the Popes do not exercise the supreme power of their Teaching Authority. For these matters are taught with the ordinary teaching authority, of which it is true to say: "He who heareth you, heareth me"; and generally what is expounded and inculcated in Encyclical Letters already for other reasons appertains to Catholic doctrine. But if the Supreme Pontiffs in their official documents purposely pass judgment on a matter up to that time under dispute, it is obvious that that matter, according to the mind and will of the Pontiffs, cannot be any longer considered a question open to discussion among theologians.
Using this to interpret paragraph 36 which I quoted above, I think I understand that (the rest of this paragraph is in my own words and I may be using some words such as 'heresy' inaccurately) whereas Darwin's theories used to be ridiculed and dismissed as incompatible with religious belief, Pius was carefully and deliberately saying that the theory of evolution is not necessarily a heresy (but neither should it be taken atheist). I think I therefore agree with the following summary from Wikipedia about Religious attitudes to On The Origin of Species:
By the early 20th century, four noted authors of The Fundamentals were explicitly open to the possibility that God created through evolution, but fundamentalism inspired the American creation–evolution controversy that began in the 1920s. Some conservative Roman Catholic writers and influential Jesuits opposed evolution in the late 19th and early 20th century, but other Catholic writers, starting with Mivart, pointed out that early Church Fathers had not interpreted Genesis literally in this area. The Vatican stated its official position in a 1950 papal encyclical, which held that evolution was not inconsistent with Catholic teaching.
For what it's worth, Fundamentalism seems to be centred in the USA. Ad Hominem isn't an argument, however it doesn't surprise me that the "dissenting view" which is cited in the OP comes from the USA. I'm surprised that a person takes this sermon as very authoritative, given that it starts with "By the authority invested in my own mind, etc."
A lot of that sermon seems to be his own opinion of or summary from the many things he has read. I won't debate its every statement in detail. The only or most reliable source in the sermon that he quotes is paragraph 37 of Humanis Generis (the next one after the paragraph 36 which I quoted above), saying,
“The faithful cannot embrace that opinion that men came from someone other than Adam and Eve or that Adam and Eve represent a collection of many first parents. Thus God created one man and from that one man, woman was created and all of mankind was created from them.” (Paragraph 37)
The full, original text is as follows:
[37.] When, however, there is question of another conjectural opinion, namely polygenism, the children of the Church by no means enjoy such liberty. For the faithful cannot embrace that opinion which maintains that either after Adam there existed on this earth true men who did not take their origin through natural generation from him as from the first parent of all, or that Adam represents a certain number of first parents. Now it is in no way apparent how such an opinion can be reconciled with that which the sources of revealed truth and the documents of the Teaching Authority of the Church propose with regard to original sin, which proceeds from a sin actually committed by an individual Adam and which, through generation, is passed on to all and is in everyone as his own.
My personal synthesis or explanation of the Church's position (I am not an expert nor authoritative, so you might instead want to ask someone who is, to explain this) is therefore:
- Evolution explains the evolution of the human body, more or less successfully
- God creates human souls
- The first human (with a soul) was Adam; Adam had original sin; all humans descend from and inherit original sin from Adam; Christ came to save us from original sin; etc.