Thousands of religions exist, each producing sincere believers, mystics, and converts convinced theirs alone is true — the sheer diversity and mutual incompatibility of these traditions is best explained by human psychology and culture generating gods in our own image, not by one of them getting privileged access to the real truth.

Why people find it persuasive

If you'd been born in Saudi Arabia you'd almost certainly be Muslim, in Thailand likely Buddhist, in medieval Europe Catholic — religious belief tracks birthplace and upbringing far more reliably than it tracks careful independent investigation, which should make any of us deeply suspicious of our own tradition's claim to uniquely privileged truth.

Important distinctions

• • Diversity of belief as evidence against any religious claim being true vs. as evidence merely that belief-formation is heavily influenced by non-rational factors.
• • Genetic/sociological explanation of why someone holds a belief vs. epistemic evaluation of whether the belief is warranted or true.
• • Total incompatibility between all religions vs. partial convergence on certain claims (a creator, moral order, transcendence) amid real disagreement on others.
• • Naive exclusivism that dismisses all other traditions as worthless vs. exclusivism compatible with genuine truth, insight, and value existing across traditions.

Christian response

• • The birthplace/upbringing observation is sociologically true and worth taking seriously, but it is a two-edged sword that the objection doesn't apply consistently: the very same genetic-explanation argument would equally undercut the skeptic's own confident naturalism (which is also, demonstrably, heavily correlated with the era, culture, and academic environment one is born into) — noting the causal origin of a belief (nearly all of our beliefs, including scientific and moral ones, have identifiable psychological and cultural causes) does not by itself show the belief is false or unwarranted; that would be a version of the genetic fallacy, since a true belief can have an unreliable-looking causal history and vice versa.
• • Religious diversity is also compatible with, and in some ways predicted by, classical theistic claims about general revelation and noetic effects of finitude and sin: if there is a real transcendent reality that humans across cultures dimly perceive through conscience, religious experience, and reasoning about the cosmos (Romans 1's claim, and C.S. Lewis's 'argument from desire' and natural law observations), but genuine special revelation with fuller, more specific content is comparatively rare and historically particular, we would expect exactly what we observe: widespread but partial and often garbled convergence on some themes (a creator, moral accountability, an afterlife, transcendent meaning) amid genuine, deep disagreement on particulars (the nature of God, the way of salvation, the person of Christ) — this is a substantive explanatory account, not merely a post-hoc dismissal of the data.
• • It's worth noting the objection, if fully generalized, is self-undermining as an argument for a positive conclusion: if the diversity and cultural-dependence of confident belief is evidence against trusting any particular confidently-held metaphysical position, it applies with equal or greater force to confident atheism/naturalism and to any specific ethical or political worldview, which are also unevenly distributed by culture and upbringing and are held with great confidence by people who disagree sharply with each other — the argument proves too much if taken as a general skeptical solvent rather than a claim specifically about religion.
• • A serious Christian response need not claim other traditions contain zero truth or value; the historic doctrine of the 'unevangelized' and much Christian intellectual tradition (from the church fathers' concept of the 'seeds of the Word' present even in pagan philosophy, to contemporary inclusivist theology) explicitly allows other traditions to contain real moral insight, genuine encounters with general revelation, and even elements of truth, while still holding that fullest, clearest, historically-anchored revelation of God's nature and redemptive plan is found in a particular, checkable historical claim (the person and resurrection of Jesus) — a claim to be evaluated on its own historical and philosophical merits, not dismissed merely because other traditions also make confident claims.
• • Ultimately the mere fact of disagreement, however sociologically striking, does not settle which (if any) tradition is correct; that requires actually engaging the specific evidence and arguments each tradition offers (historical evidence for the resurrection, philosophical arguments for classical theism, comparative textual and moral analysis) rather than inferring from the existence of disagreement alone that investigation is pointless or that all positions must be equally (un)warranted — we don't reason this way in any other domain of deep, persistent expert disagreement (philosophy, ethics, even some areas of science), where sustained disagreement is taken as reason for humility and more inquiry, not for concluding no position could ever be warranted.

Christian counterresponse

This connects back to the deeper divine-hiddenness discussion, and the honest answer is that it remains one of the harder aspects of religious epistemology; the theist's resources here (general revelation reaching everyone in some form, judgment based on response to the light one has, possible postmortem opportunity, God's providential involvement in each person's specific historical and cultural circumstances in ways not fully transparent to us) are substantive but do not fully dissolve the discomfort of the unevenness of access to explicit revelation, which is a real cost that has to be weighed against the positive case for the specific historical claims of Christianity, rather than eliminated entirely.