I'll offer 3 critiques
1. A leap of faith too far
For purposes of this post I'll use as a working definition of faith the one proposed by @curiousdannii - reliance on something because of its past behavior (the popular refrain that faith is belief without evidence is a strawman--see further discussion in my post here).
All life forms with which we have experience result from one or more previously-existing life forms; we do not have evidence of life (much less self-replicating life) emerging from non-life by natural processes alone.
All of examples of specified complexity with which we have experience are the product of intelligent minds; we do not have evidence of specified complexity emerging from natural processes.
This does not mean these things cannot happen - it means we don't have evidence to support that they happen. To accept a priori that methodological naturalism provides the best avenue for answering the question of the origin of life is to decide on the very variable under consideration before even looking at the evidence (not very scientific!).
Trusting in methodological naturalism to deliver results in the study of origin of life is an act of faith.
- The scientific method, as well as theological systems that accept the ongoing nature of revelation, have built in systems to allow for correction when errors are made.
- Naturalism is a binary philosophical assumption that can either be accepted or rejected. It cannot correct itself - the most it could ever do is fail enough times that people choose to discard it.
I can see why people would put faith in the first two; it is unclear to me why anyone would put so much faith in the latter.
Those who suspend judgement on the matter of the origin of life may be intellectually consistent, but those who actively believe that naturalism will eventually produce a solution to the origin of life problem are making a god-of-the-gaps argument: I can't yet answer this question, therefore I assume naturalism will eventually produce an answer. This is a faith-based position, relying upon prior results from methodological naturalism (whatever those might be) in order to trust it.
This is why Frank Turek is famous for his claim I don't have enough faith to be an Atheist.
Doug Axe famously argued that the sequence space for protein folds is too vast for successful innovation by chance, indicating that only approx. 1 in 10^78 possible DNA variations is viable.
Since there have been (generously) 10^42 life forms in the history of earth, we would have to replay the entire history of life on earth about 1,000,000,000,000,000,000,000,000,000,000,000,000 times in order to get just one new protein fold to come into being by chance. Adding in the need for multiple protein folds, to say nothing of a self-replicating mechanism, would make the chance-hypothesis even weaker. This objection is relevant to both origin-of-life and evolution-of-life studies. For abiogenesis to work, we would need multiple successful protein folds, and a self-replicating mechanism.
If we grant that there are 10^23 habitable planets in the universe, and the earth represents an "average" habitable planet, even then, the entire universe would not give us 10^78 opportunities for an accidental life form to emerge and replicate itself even once. (10^23 * 10^42 = 10^65).
Facing otherwise insurmountable odds, some philosophers have turned to multiverse hypotheses. While I take no issue with the possibility that more than one universe could exist, this is not a scientific theory, it's a philosophical theory (it's non-falsifiable), and it is vulnerable to the same difficulties discussed in section 1 of this post.
3. Occam's Razor
Upon re-reading the original question, I see that my response left out a significant dimension: this question is addressed to Christians, who already believe in God.
To those who already believe in God on other grounds, abiogenesis is an unnecessary and redundant hypothesis. Abiogenesis (at least as it is usually presented) is an argument that is designed (see what I did there?=)) to explain the accidental origin of life. Those who believe in a Divine Creator on the basis of sacred texts, the witness of the Holy Spirit, objective moral truths, etc., conclude that life is not an accident. Abiogenesis requires believing in the fantastically improbable in an effort to avoid believing in a Creator (no but really--consider multiverse models that are willing to accept--no matter how unlikely--the reality of every scenario imaginable except one in which God exists). Those not pre-committed to such naturalistic conclusions could amusingly reverse Laplace's own statement to argue against him: when it comes to abiogenesis, I have no need of that hypothesis.
The first two sections of my argument show why abiogenesis is a weak hypothesis, and ought to be treated skeptically on probabilistic grounds. The third section of my argument acknowledges that a belief in God can be (and usually is) reached through independent means. To those who accept the teaching of Genesis that God created the heavens & the earth (see Genesis 1:1), theories on the accidental origin of life fail the Occam's razor test--they multiply hypotheses beyond necessity.
For my own part, I came to a belief in God for reasons unrelated to the structure of cells. A study of biology reinforces that belief on teleological grounds, and perhaps more importantly, increases my respect for the Creator.
Given the available evidence, an intelligent mind appears to be the most viable explanation for the existence of specified complexity in life - it is the only theory that can point to real-world examples where the proposed source has actually produced the effect in question.
I also take no issue with the possibility that the Creator could use natural processes (like a programmer uses the natural properties of silicon) to carry out His intentions. This wouldn't make the Creator any less powerful--it would just mean He's smart. I lose no respect whatsoever for the Wright Brothers by discovering how they did their work.
I see no conflict between respect for the Creator and an awareness of how He performed some small portion of the creation.
The teleological argument from biological specified complexity is an argument for an intelligent mind behind creation, not an argument for many of the specific theological claims about God. Teleology is often used to establish that there is a Creator; understanding the nature & intentions of the Creator is the business of theology.
(teleological arguments--from the Greek telos, meaning "end" or "goal", use features of the universe that show evidence of being designed to argue for the existence of a designer)
Response to objections
The probability section seems to ignore (a) the possibility that DNA started off simpler
My calculations required only 1 protein fold...hard to ask DNA to deliver a result much simpler than that.
(b) that natural selection guides the randomness
This would be a novel theory of evolution, and is not consistent with the modern synthesis of Darwinism, which holds that natural selection acts upon random mutation. Random mutation is just that, it's random. Natural selection merely favors/disfavors from what it is given to work with. It cannot guide which mutations occur, only which mutations survive.
(c) that all mutations may not be equally likely or even possible
Axe's work focused on viable combinations vs. possible combinations.
(d) mutations of viable variations are much more likely to be viable variations themselves
While this may be true, it would be stronger if defended with evidence. In any event, this would be applicable to the evolution of existing life; it has nothing to do with abiogenesis.