As far as I’m concerned the FTA is just a reframing of a very old argument. Namely “The universe is so amazing it must have been created”. It brings no evidence to the table to support it. And it also drags poor probabilities into an argument in which they have no place.
That actually doesn't work for most religions or most arguments. For example, a common interpretation of Islam (at least during the late medieval and early modern period), or perhaps I should say of the Quran and ahadith, was that finding order in the cosmos placed limitations on God. This view exists also in the Old Testament, but by the time the Church had begun to climb back up to the academic/intellectual status of the Roman empire (in other words, by the time Western Christians were in a position to develop natural philosophy, the precursor to science), the Church quickly wedded itself to Aristotelian philosophy and thanks to the factors like the Protestant revolution quickly developed natural philosophy. In other words, we can't see how constraining cosmology was to the intellectual/academic development within Christianity because by the time Christians were at the point to develop arguments based upon the nature of the universe Scholasticism developed in the West while the East was already mostly conquered and continued to shrink (FYI- a common misconception is that part of the reason the Church adopted the view that the Earth was the center of the universe was because this was a good position, rather than the notion actually held: that this was the lowest position).
In the East, not only was such a view absent from most if not all traditions, the majority viewed the material world as mostly negative and the cosmos unchanging or cyclical.
The first developed "proofs" (arguments) for God, such as Anselm's, Descartes', etc., made no reference to cosmic design. The scholalistics followed Aristotle in reasoning about causality (his 4-fold division, out of which the final cause naturally was attributed to God), and the first real argument for design of the type you refer to isn't until Hume's
Dialogues Concerning Natural Religion. One can certainly quote-mind various texts and see words like order or how God's works are so magnificent because God is magnificent, but these are no more arguments than is Hamlet's description of the cosmos when first he meets up with Rosencrantz and Guildenstern (minus the ending- "and yet to me, what is this quintessence of dust? Man delights not me").
Another difference is that fine-tuning isn't just an argument for a designer. It's a simple fact of physics, that physicists hold to be true whether they regard it as a problem to be explained, don't care, or believe it to be evidence of design. The question isn't
whether our universe is fine-tuned, it's what this might entail, could entail, and cannot entail.
