Does a man of sense run after every silly tale of witches or hobgoblins or fairies, and canvass particularly the evidence? I never knew anyone, that examined and deliberated about nonsense who did not believe it before the end of his inquiries. J. Y. T. Greig, ed. The Letters of David Hume (Oxford, 2011), 1:350.
Clearly there's something right about this statement. The insinuation, however, is that Christian apologists have a double standard. Why their selective, one-sided fixation on Christianity, while ignoring so many other candidates? This raises a number of issues:
i) As a matter of fact, Christian apologists do evaluate rivals to Christianity, or orthodox Christianity. They evaluate Islam, Hinduism, Buddhism, and the cults. Protestant apologists evaluate Catholicism. And so on.
ii) The issue is by no means unique to religious claims. It's true regarding factual claims generally. Historians and biographers wrestle with competing interpretations. Why did Dean Martin and Jerry Lewis really break up? Suppose I don't care. Conversely, suppose I do care about the medical options for an ailing relative? Is it arbitrary for me to be more interested in nailing down some factual claims rather than others? Hardly.
iii) Apropos (ii), is it incumbent on me to have an informed opinion about the Loch Ness monster, or whether extraterrestrials have made contact with earthlings? What difference does it make to my life whether or not the Loch Ness monster exists?
Likewise, suppose extraterrestrials have made contact with earthlings, but I don't believe it. My disbelief has no impact on their behavior. They will continue to do whatever they are doing regardless of my belief or disbelief in their existence. Even if they exist, everything happens in my life the same way as if they don't exist. Unless and until they take control, the status quo is indistinguishable from their nonexistence.
However, the same can't be said for Christianity. For one thing, there's the Christian doctrine of the afterlife. If Christianity is true, then my beliefs and behavior do matter in the long run.
iv) There's a difference between examining evidence for a general kind of thing, and evidence for any particular candidate. There's a difference between establishing the category of the supernatural, and proving or disproving the existence of each and every candidate.
v) Apropos (iii), I don't have to run through a list, proving or disproving every particular candidate, to prove the reality of the supernatural. A few good examples will suffice. And that's a very significant finding. A world in which supernatural events and entities of any kind exist is a very different kind of world than naturalism.
vi) In attempting to prove or disprove the general proposition, it's by no means arbitrary to confine myself to the best-attested candidates. And that starting-point is scarcely confined to religious claims. To establish the existence of a supernatural realm, it's only rational to consider candidates with the best evidence. And do the same thing were I attempting to confirm the exists of a rare animal. I'd begin with credible sightings.
vii) It isn't always necessary to directly disprove a claim to successfully disprove it. For instance, there's direct evidence that Newtonian physics is false. But even apart from that, if there's direct evidence that Relativity is true, and if the concepts of time and space in Relativity are incompatible with the concepts of time and space in Newtonian physics, then that indirectly falsifies Newtonian physics.
By the same token, if Christianity is true, then that at one stroke falsifies Islam and paganism. It isn't necessary to independently disprove the existence of every heathen god and goddess, for if their existence is incompatible with Christian theism, then demonstrating Christian theism ipso facto eliminates any and all contrary contenders.