They do a lot of great work ... to bad they're on the wrong side of the Flat Earth issue .

Abelard did get a bit of a bad rap though.  He actually pioneered and was the precursor to the scholastic method, with his work Sic et Non (Yes and No).  He had as his pupil Peter Lombard, famous for the Sentences, which in turn heavily influenced St. Thomas.

When his works were first submitted to Rome for condemnation, there was no condemnation made, but instead he was just asked to recite the Athanasian creed.

He was the first to challenge St. Augustine's incorrect teaching regarding the fate of infants who die unbaptized, and he ended up doing a great service to the Church rather than letting this error continue.

I think that's why he got into trouble, especially with St. Bernard, because he came across as haughty by subjecting everything to scrutiny rather than accepting it with simple reverence.  He had no problem challenging St. Augustine's thinking when he felt it was warranted.  St. Bernard on the other hand adopted a more mystical approach.  When asked about Baptism of Desire, for instance, St. Bernard simply said that he would rather be wrong with St. Augustine than right on his own ... but never really addressed the issue theologically.

Here's from Catholic Encyclopedia:

With regard to the relation between reason and revelation, between the sciences — including philosophy — and theology, Abelard incurred in his own day the censure of mystic theologians like St. Bernard, whose tendency was to disinherit reason in favour of contemplation and ecstatic vision. And it is true that if the principles "Reason aids Faith" and "Faith aids Reason" are to be taken as the inspiration of scholastic theology, Abelard was constitutionally inclined to emphasize the former, and not lay stress on the latter ... and though the thirteenth century, the golden age of scholasticism, knew little of Abelard, it took up his method, and with fearlessness equal to his, though without any of his flippancy or irreverence, gave full scope to reason in the effort to expound and defend the mysteries of the Christian Faith.

So, partly his contemporaries, due to their bent toward "mystic" theology, object to his very method ... as he was ahead of his time with it.  This notion that it was irreverent was largely exaggerated by his contemporaries because the were not accepting of his methods, which then were later adopted by the scholastics.  He did in fact hold to the primacy of faith aided by reason, as stated above.

I don't think that he was actually irreverent and flippant, whereas the scholastics adopted the same methods but without that flippancy, I believe that this was simply because he was ahead of his time in pioneering the scholastic method, and this was due to perception by his contemporaries that the method was irreverent.  Again, cf. St. Bernard's "theological" analysis of BoD consisting of "I'd rather be right with Augustine than wrong on my own."  Abelard evaluated everything on its own merits, and he did a great service by correcting a mistake by St. Augustine that otherwise might have carried on much longer ... due to this fear of "questioning" St. Augustine.  In fact, the Church had to condemn the proposition that the teaching of St. Augustine is to be preferred over that of the Magisterium.  When the Church condemns a proposition like that, it's not hypothetical but because there were actually people saying this.

So, St. Bernard charged Abelard with "savoring" (sapit) of Arianism, Nestorianism, and Pelagianism.  He couldn't say that they were but merely that they "savored" of it.  But the reason for this perception was due to the "subtlety" of Abelard, where he made lots of "distinctions" and the theological world at the time did not really think in terms of distinctions.

Abelard was in a very real sense the father of scholasticism.

St. Bernard's perception of him (as quoted above) was actually misguided to to his embrace of "mystic theology":

The Abbot Abelard lifts his head to heaven, examines the lofty things of God, and returns to report to us the ineffable words which it were not lawful for a man to utter; and while he is ready to render a reason for all things, even for those which are above reason, he is presuming against both reason and faith; since what can be more contrary to reason than to strive by reason to go beyond reason? And what could be more contrary to faith than to refuse our belief to that which we cannot attain by reason?

This perception was created by the fact that Abelard was taking revealed truths and applying logic and reasoning and syllogisms to it.  There was not "refusal to believe that which we cannot attain by reason."  Abelard thought no such thing.  But it was perceived that way, and was perceived as temerity to actually reason about revealed truths the way he did.  But that way was in fact what came to be known as the scholastic method.

Now, Abelard was indeed arrogant, which led to a notorious moral fall, but he had massive followings and had a tremendous influence.  He had more friends than enemies.  But part of his arrogance and vanity came from his talents.  From Catholic Encyclopedia:

There can be no doubt that Abelard's career as a teacher at Paris, from 1108 to 1118, was an exceptionally brilliant one. In his "Story of My Calamities" (Historia Calamitatum) he tells us how pupils flocked to him from every country in Europe, a statement which is more than corroborated by the authority of his contemporaries. He was, in fact, the idol of Paris; eloquent, vivacious, handsome, possessed of an unusually rich voice, full of confidence in his own power to please, he had, as he tells us, the whole world at his feet.

That Abelard was unduly conscious of these advantages is admitted by his most ardent admirers; indeed, in the "Story of My Calamities," he confesses that at that period of his life he was filled with vanity and pride. To these faults he attributes his downfall, which was as swift and tragic as was everything, seemingly, in his meteoric career.

Here's a good writeup about Abelard, and this section is about his theology.  You'll find at the end a citation wherein he condemns precisely those errors he was accused of.  He was confused with what he calls the pseudo-dialecticians.  What he's articulating is precisely what would later become the scholastic method:
https://plato.stanford.edu/entries/abelard/

Abelard held that reasoning has a limited role to play in matters of faith. That he gave reasoning a role at all brought him into conflict with those we might now call anti-dialecticians, including his fellow abbot Bernard of Clairvaux. That the role he gave it is limited brought him into conflict with those he called “pseudo-dialecticians,” including his former teacher Roscelin.

Bernard of Clairvaux and other anti-dialecticians seem to have thought that the meaning of a proposition of the faith, to the extent that it can be grasped, is plain; beyond that plain meaning, there is nothing we can grasp at all, in which case reason is clearly no help. That is, the anti-dialecticians were semantic realists about the plain meaning of religious sentences. Hence their impatience with Abelard, who seemed not only bent on obfuscating the plain meaning of propositions of the faith, which is bad enough, but to do so by reasoning, which has no place either in grasping the plain meaning (since the very plainness of plain meaning consists in its being grasped immediately without reasoning) or in reaching some more profound understanding (since only the plain meaning is open to us at all).
...
There is a far more serious threat to the proper use of reason in religion, Abelard thinks (Theologia christiana 3.20):

Quote

Those who claim to be dialecticians are usually led more easily to [heresy] the more they hold themselves to be well-equipped with reasons, and, to that extent more secure, they presume to attack or defend any position the more freely. Their arrogance is so great that they think there isn’t anything that can’t be understood and explained by their petty little lines of reasoning. Holding all authorities in contempt, they glory in believing only themselves—for those who accept only what their reason persuades them of, surely answer to themselves alone, as if they had eyes that were unacquainted with darkness.

... and here's some more about the condemnation of Abelard (from the same source).  Abelard got the "Father Feeney" treatment.

By the mid-1130s Abelard was given permission to return to Paris (retaining his rank as abbot) and to teach in the schools on the Mont Ste.-Genevieve. It was during this time that his theological treatises were brought to the attention of Bernard of Clairvaux, who objected to some of Abelard’s conclusions as well as to his approach to matters of faith. After some inconclusive attempts to resolve their differences, Abelard asked the archbishop of Sens to arrange a public dispute between himself and Bernard on 3 June 1140, to settle their disagreements. Bernard initially refused the invitation on the grounds that one should not debate matters of faith, but then accepted it and, unknown to Abelard, arranged to convene another commission of enquiry to review Abelard’s works on suspicion of heresy. When Abelard discovered that there was no debate but instead a kangaroo court, he refused to take part, announcing his intention to appeal to the Pope directly. He walked out of the proceedings and began travelling to Rome. The Council condemned nineteen propositions it claimed to find in his works and adjourned. Bernard launched a successful campaign petitioning the Papal Court before Abelard was out of France; a letter from the Pope upholding the decision of the Council of Soissons reached Abelard while he was at Cluny; Abelard was ordered to silence. By all accounts Abelard complied immediately, even meeting peacefully with Bernard in reconciliation. Peter the Venerable, the abbot of Cluny, wrote to the Pope about these matters, and the Pope lifted Abelard’s sentence. Abelard remained under the protection of Peter the Venerable first at Cluny, then at St. Marcel, as his health gradually deteriorated. Abelard died on 21 April 1142. His body was interred at the Paraclete, and today is (with Héloïse) in Père Lachaise cemetery in Paris.

With all due respect to the holy St. Bernard, he was in fact mistaken, and Abelard would be vindicated later when scholasticism would eventually be declared to be THE theological system of the Church.

Of course, in the realm of moral theology, Abelard was accused of being excessively subjectivist, but even there I think he was misunderstood.  He simply called out that evil (sin as sin) was defined by the formal intent to offend God rather than by the action itself.  So, for instance, if I pick up a $100 bill from a table thinking that it's mine, I commit no sin, no offense against God.  But he does appear to have undervalued the objective injustice of the rightful owner of the $100 bill.

So Kolbe's citation of what St. Bernard wrote against Abelard was misapplied in that St. Bernard was mistaken about the inappropriateness of Abelard's methods and approach.