Note: The following post is a guest post by SO commenter Angra Mainyu.
In this post, Jerry Coyne made a some ethical and metaethical claims, as well as some claims about compatibilists. In this post, I would like to address some of his claims about compatibilists.

I think the failure of many compatibilists to give explicit definitions of the term is that so doing would would expose the intellectual vacuity of their arguments. You’ll look in vain in Dennett’s piece for his definition of free will.

First, Coyne has provided no good reason to think that the arguments of compatibilist philosophers are generally intellectually vacuous, let alone that they know that.
Second, compatibilists who don’t provide a definition of “free will” may simply not have one that approaches the common meaning of the term “free will” enough for the purposes of philosophical discussion, or alternatively don’t find it necessary in the context in which they’re making their points. Why would that be a problem?
For example, a philosopher may reflect on the expression “free will” – as it’s usually used -, and reckon that free will does not require indeterminism, without ever defining “free will”, just as – say -, a philosopher may reflect on the expression “morally good” (or “kind”, for example), and reckon that moral goodness (or kindness) does not require the existence of God, without ever defining “morally good” (or “kind”), etc.
Why would that be a problem in the case of free will?
Coyne does not say. But let us turn to Coyne’s comparison between compatibilism and sophisticated theology, and the charges he raises against compatibilists therein:

Both redefine old notions (Biblical literalism or contracausal free will) and claim nobody believes in them any more. Like scripture is for Sophisticated Theologians™, so is free will for compatibilists: both have become metaphors for more recent notions.

First, it is not the case that compatibilists generally claim that nobody believes in contracausal free will anymore.
I don’t know if some compatibilists have that belief, but it certainly isn’t a common one. In fact, Coyne has not provided any evidence that a single compatibilist philosopher – let alone most, not to mention all – claims that there has been a significant shift in commonly held beliefs about free will among the public, from having belief in contracausal free will to not having such belief.
Second, Coyne provides no good reason to believe that compatibilist philosophers redefine a notion of free will.
One of the most common disagreements between compatibilists and incompatibilists is about the meaning of the expression “free will”, in its usual sense. Compatibilists generally hold that the expression “free will”, in its usual sense, does not mean contra-causal free will and does not entail indeterminism, and so – for example -, a statement such as “Coyne wrote the post of his own free will” does not attribute contra-causal free will to Coyne.

The definitions of free will, like that of Sophisticated Gods, are concocted post facto, after compatibilists have decided in advance that their task is not to find the truth, but to buttress a conclusion they want to reach (i.e., we have free will)

First, Coyne provides once again no good reason to even suspect that his claim about compatibilists might be true.
Second, compatibilist philosophers usually have already worked on the task of finding the truth about whether the expression “free will” is such that attributing free will to an agent involves making a claim about some contra-causal entities (or properties, things, etc.), indeterminism, etc., and have concluded that it does not involve any of that that.
Granted, incompatibilist philosophers disagree, and the debate goes on. But that does not remotely suggest that the charge might be true.

Both set humans aside as special—different from other animals (soul or free will)

It’s not clear to me why Coyne believes compatibilism is committed to setting humans aside, but he is mistaken.
In fact, while different compatibilist philosophers may hold different views, a compatibilist may well hold that change between species was gradual, and also that different animals (humans or not) have different degrees of freedom.
Incidentally, while Coyne rejects moral responsibility, immorality, and so on, he holds that there is bad behavior.
What if someone were to charge him with setting aside humans – or humans and all other animals he believes are capable of bad behavior – as “special-different from other animals”?
Granted, he might give an answer along the lines of ‘organisms that can engage in bad behavior gradually evolved from organisms that can’t’ (what else might he reply?), but that is similar to a compatibilist replying that organisms that have free will gradually evolved from organisms that do not have free will.

In both cases academic doyens (theologians or philosophers) feel that it’s dangerous for the public to know the truth (about God or about determinism).

Actually, Dennett and some other compatibilist philosophers believe it would be negative if the public at large were to hold the false belief that there is no free will. But Coyne’s expression seems to suggest that compatibilists believe something like ‘It would be dangerous for the public to know the truth about determinism’, which is false of course.
Still, perhaps Coyne didn’t mean that, but rather, he meant something along the lines of:
a. Theologians believe that it’s dangerous for the public to believe that God does not exist, but it is true that God does not exist (regardless of whether those theologians believe that God exists)
b. Compatibilist philosophers believe it’s dangerous for the public to believe that there is no free will, no moral responsibility, no immoral behavior, etc., even though it is true that there is n free will, no moral responsibility, no immoral behavior, etc. (regardless of what those compatibilist philosophers believe that there is free will, moral responsibility, immoral behavior, etc.)
However, if he meant that, there are at least two difficulties:
The first one is that he made a misleading statement, and is likely to be misinterpreted by many readers.
The second and bigger one is that he failed to show that there is no free will, no moral responsibility, and/or no immoral behavior. Furthermore, he’s not provided any good arguments in support of those views.

To get there, both camps simply redefine terms, so that both “God” and “free will” become notions that don’t correspond at all to how they’ve been understood through history. Compatibilists will say this is okay, but to me it’s like saying, “Jerry Coyne loves dogs—if you redefine dogs as ‘members of the Felidae’.”

Coyne appears to be implying that compatibilists are deliberately redefining terms.
Anyone mildly familiar with the debates between compatibilist and incompatibilist philosophers ought to realize that the implication is false.

Both dismiss science as either irrelevant or inferior to philosophy for solving the Big Question at hand (free will or the existence of God).

Some compatibilist philosophers correctly point out that experiments intended to shed light on how the brain works, and in particular, how it makes choices, are not relevant to answering questions such as whether the usual expression “free will” is such that attributing free will to an agent entails the claim that her actions or choices are not determined by previous events, states, etc.
Those are matters of conceptual analysis.
This is not to say that experiments may not shed light on such matters. But those would have to be experiments designed to assess how people use the words.
In fact, some experimental philsophers are working on that, including compatibilists – like Eddie Nahmias -, and incompatibilists – like Joshua Knobe.
At this point, the results of the experiments vary widely depending on how the questions are worded, but it may well be that in the future, such research will provide clear evidence in support of one of the sides – and, in my assessment, the answer will favor compatibilism.
Regardless, given context, it is clear that Coyne is implying that compatibilist philosophers are dismissing science – at least partially – in an improper fashion. But there is no indication of that.