It might perhaps be a fatal to fideism to notice that if one really believes that God cannot be known by reason, he can build a rather impressive and extensive natural theology from that principle. For example, if we were in earnest that God is “he who the human mind cannot know” we can immediately prove he is not a body, for we certainly know what a body is. We can also immediately prove that God is not in a genus, for genera are tools by which human beings come to know (we need to know in this way because our intellect comes to know from imperfect concepts). If we know God is not in a genus, we could prove that he is one, for if there were two of his nature there would be a genus. Similar considerations wold prove his total simplicity. Further, we could prove that we must speak about God analogously: for if we spoke of him univocally, he would be in a genus; and if we spoke of him equivocally, we would know nothing of him- but we know he is what the human mind cannot know, etc.
In other words, one could reproduce most of what St. Thomas proves in his natural theology from a fidesitic principle. Fideism might make thomism even easier, since you wouldn’t have to bother proving God’s existence (in fideism, the existence of God is simply a given). Fideism is stuck with having to defend why it, along with natural theology, concludes to a being with identical attribuites as God- and even with the same name- but somehow is still speaking of a distinct being.