The MP's definition of fideism is this:
B. Fideism: Put your trust in blind faith. Submit, obey, enslave your reason to what purports to be revealed truth while ignoring the fact that what counts as revealed truth varies from religion to religion, and within a religion from sect to sect.
Kierkegaard (SK) was not a fideist by this definition. In fact, his career was dedicated to overthrowing the list of alternatives the MP gives in his post:
A. Rationalism: Put your trust in reason to deliver truths about ultimates and ignore the considerations of Sextus Empiricus, Nagarjuna, Bayle, Kant, and a host of others that point to the infirmity of reason.
[we've seen B above].
C. Skepticism: Suspend belief on all issues that transcend the mundane if not on all beliefs, period. Don't trouble your head over whether God is or is not tripersonal. Stick to what appears. And don't say, 'The tea is sweet'; say, 'The tea appears sweet.' (If you say that the tea is sweet, you invite contradiction by an irascible table-mate.)
D. Reasoned Faith: Avoiding each of the foregoing options, one formulates one's beliefs carefully and holds them tentatively. One does not abandon them lightly, but neither does one fail to revisit and revise them. Doxastic examination is ongoing at least for the length of one's tenure here below. One exploits the fruitful tension of Athens and Jerusalem, philosophy and religion, reason and faith, playing them off against each other and using each to chasten the other.
The MP, as might be expected, advocates option D. But SK would say that option D isn't really the neutral compromise between faith and reason it appears to be. It actually embodies a deep confusion about human existence that prejudices the argument. Notice that option D includes an existential conclusion: One is advised to hold beliefs "tentatively." But while it includes an existential conclusion, it does not include any existential premisses. It's one premiss is an assertion about reason in the abstract:
Reason is too weak and confused to discover the truth about the world and how we should live in it.
What is significant about the premiss is not its content but its form. It is an assertion about reason in the abstract, and therefore, according to SK, only abstract conclusions can be drawn from it. But the decision about whether I should embrace faith is anything but abstract; it is as concrete and subjective as it could be, it is, in other words, existential. The attempt to draw an existential conclusion from purely abstract premisses cannot be done; this is why the MP's conclusion must be that beliefs are held "tentatively", or, in other words, without any existential decisiveness. This is really just a restatement of the fact that abstract reason cannot issue in existentially decisive conclusions.
But the question of faith is a question that is existentially decisive in its nature. SK's point was that modern thought begged the question of faith in its very constitution, since it accepted that "reason" is synonymous with "objective thought", or in other words, thought abstracted from the exigencies of human existence. Objective thought is "thought without a thinker", or, in other words, thought without any existential premisses.
SK contrasted "objective thought" with what he called the "subjective thinker." Notice "thought" is an abstract something, but that a thinker is a subjective someone, existing in some time and place. What SK tried to do was repair the breach in existence that was created by modern thought. Classical thought suffered no such breach, which is why SK reaches back to Socrates so often in his writing. Socrates was the prototypical subjective thinker or, rather, a thinker who never suffered the dislocation between subjective and objective thought.
Socrates would never say something like "Reason is too weak and confused to discover the truth...". For one thing, it is self-defeating, since if reason is too weak and confused to discover the truth about the world, then one of the truths it is too weak and confused to discover is itself, since the very proposition is a truth about the world. What Socrates would and did say was "I know that I do not know," which is an excellent example of an existential premiss that can get subjective reasoning rolling. If I do not know, then one of the things I don't know is whether or not anyone else knows, or whether or not there is a truth about the world that can be known. So I am presented with the choice of remaining static in my ignorance, or actively seeking out those who might know and might be able to teach me. Ironically, one of the things I do know is that I do not wish to remain ignorant, so I will seek out those presumed to be wise. This is a chain of subjective reasoning, starting from an existential premiss, and issuing in an existential conclusion. This is a simple example of subjective reasoning; Kierkegaard's analysis of the subjective reasoning involved in the faith decision is profound and well worth the reading of his Philosophical Fragments and Concluding Unscientific Postscript.
SK was far from advocating "blind faith" or the "enslavement" of reason to revealed truth. What he passionately wished to communicate was a recovery of subjective reasoning; and the truth that faith, if it is to be fairly considered or even understood for what it is, must be considered in a mode of subjective rather than objective thought. SK's corpus may be thought of as therapy for those suffering the modern rupture between the objective and the subjective, so that they may recover the authentic mode of subjective thinking (which is really human thought in its true form), and so truly face the question of faith. The question of faith, presented in its objective form, is never really presented at all.