The slander involves taking an out-of-context quote and making it mean pretty much the opposite of what Kant was trying to say. Dr Sanity seems to be largely relying on Stephen Hicks who writes:
By the late 1700s religious thinkers had a choice—accept evidence and logic as the ultimate court of appeal and thereby reject their deeply-cherished religious ideals—or stick by their ideals and attack the whole idea that evidence and logic matter. “I had to deny knowledge,” wrote Kant in the Preface to the first Critique, “in order to make room for faith.” “Faith,” wrote Kierkegaard in Fear and trembling, “requires the crucifixion of reason”; so he proceeded to crucify reason and glorify the irrational.(as an aside, I suspect that Kierkegaard is also being taken badly out of context here).
UPDATE: My interpretation of Kant's sentence was completely wrong due to the fact that I carelessly read "reasoning" where the translated word is "knowledge" (In my defense, it was well past my bed time when I wrote that post). The word change completely changes the meaning of the phrase, but it still does not support Hicks's revisionism. I stand by everything in the following except the parts where I am trying to understand what Kant meant.
I'll write another post where I take the novel approach of actually presenting the sentence in context.
Kant is not saying what the a simple reading of this sentence suggests: that he has to ignore the facts because they make it hard to believe in God. The reasoning that Kant is referring to is not reasoning that tries to show the non-existence of God --he is referring to reasoning that tries to show the existence of God.
In Kant's time, there was a common belief that reasoning could be used to prove all truths, including the existence of God. There were various "proofs" of the existence of God considered persuasive by influential thinkers. Although there were some who didn't buy any of the proofs that they had heard, it was widely believed that the question of God's existence could be settled, one way or another, by logical proof. Kant rejected this idea.
What Kant is saying in that quote is that since reason can never, even in principle, prove the existence of God we should give up the attempt and rely instead on "faith", by which he means another way of arriving at the knowledge of God.
More generally, Kant argued that we have different ways of arriving at different kinds of knowledge. There is no single faculty that is the ultimate source of all knowledge. This is in contrast to a very popular view in his day (associated with Descartes) that pure reason was the ultimate arbitrator of knowledge. In fact the title of the book that contains this out-of-context quote is "A Critique of Pure Reason".
Kant was, in fact, correct. I've written before about the program of the Logicists who tried (and failed) to disprove one of Kant's examples by proving that all of mathematics can be derived from pure logic. Mmathematics seems to be as close to pure reason as you can get and yet the axioms of mathematics cannot be derived from pure logic. Logic cannot tell you that if A is less than B and B is less than C, then A must be less than C. This is knowledge that you must be able to acquire through some faculty other than logic.
So, it is not true that Kant was endorsing religious faith based on closing ones eyes and shouting "I can't hear you" over and over.
But lets get back to that Stephen Hicks quote: "By the late 1700s religious thinkers had a choice—accept evidence and logic as the ultimate court of appeal and thereby reject their deeply-cherished religious ideals—or stick by their ideals and attack the whole idea that evidence and logic matter". This is wrong in two important ways.
The first mistake is in the false dichotomy. Hicks offers the choices (A) accept evidence and logic as the ultimate court of appeal or (B) drop the idea that evidence and logic matter. Obviously there is a third option, one accepted by most rational people today, (C) accept that logic and evidence matter but don't assume that they can settle every question.
The other mistake is Hicks's assertion that the intellectual crisis that Kant was responding to was a crisis of "deeply-cherished religious ideals". Religion wasn't even under serious intellectual attack at the time. There were certainly rigorous debates about the existence of God, but the atheists had made no more progress in the debate than the theists had. It was an intellectual crisis in science and not any crisis in religion that motivated Kant to produce a work that arguably inspired post-modernism. I don't believe that Kant was even particularly religious.
What was under serious intellectual attack was not the deeply-cherished religious ideals but the deeply-cherished ideal that evidence and logic is the ultimate court of appeal. The empiricists such as Bishop George Berkeley (CofE) and David Hume had fairly demolished the idea that science (or any body of belief) could ever be at the same time (1) about the real world, (2) based entirely on evidence and logic, and (3) certain. Hume, in particular, had already killed this eighteenth-century concept of science but in Kant's day they still kept it around like the corpse in "Weekend at Bernie's". Kant's "Critique of Pure Reason" was an attempt to read the last rites to this false conception, but he wasn't entirely successful. The corpse continues to be dragged out for all the parties even today.
UPDATE: I've done a better explanation of the quote here.