This argument primarily comes down to arguing that because a certain category has blurry boundaries that we shouldn't use it. This confuses having blurry boundaries with being useful.
The problem is not with the category having blurry boundaries, but with the fact that it (arguably) leads to grossly miscalibrated heuristics for evaluating beliefs. Such bad heuristics then end up being not just widely used by individuals, but also built into the system of government.
There is one especially common pattern in ideological disputes where such heuristics can be catastrophically bad. Suppose side A in a dispute claims a religious basis for its beliefs, which are however not derived from the religious axioms in some strict logical manner, but in fact the religious stuff serves only as the supporting narrative for what is just accumulated conventional wisdom and tradition. Suppose then that the opposing side B claims that its beliefs are a product of pure rational thinking, whereas in reality their supposed "rational thinking" or even "science" is a mere rationalization for their ideology -- which is, at bottom, just another collection of human biases and metaphysical beliefs, although the latter are not about any anthropomorphic entities.
In situations of this sort, it is not at all unusual that the beliefs of the side A about practical issues are in fact reasonably close to reality, while the beliefs of the group B are grossly delusional and incredibly destructive if applied in practice. But the "religion" heuristic can make a wannabe rational thinker side with B for the ultimately silly reason that their metaphysics doesn't involve anthropomorphic entities. (Even if the entities it does postulate are just as fictitious, the resulting reasoning equally fallacious, and the ultimate practical implications far crazier.)
Now, of course, contemporary examples of this pattern are likely to be ideologically charged to an extreme degree. But for a distant and hopefully uncontroversial example, imagine living in some country circa 1930 where there is an ongoing struggle for power between, say, some run-of-the-mill Christian conservatives and Communists. The religion heuristic might tell you that the latter, whatever their faults, are at least attempting to base their worldview on rational thinking, so they can't possibly be the worse choice -- even though they are in fact, by any reasonable measure, the more insane side by orders of magnitude. (And unsurprisingly, around that time plenty of purported rational thinkers did end up supporting the crazier side in disputes of this sort.)
Also, to end this comment on a more controversial note, what I find really scary is that the modern "separation of church and state" principle, which uses the "religion" heuristic for determining who is allowed to influence the workings of the government, is actively selecting for ideologies that are most adept at hiding their metaphysics below layers of purportedly pure rational (or even "scientific") thinking. While this is admittedly a controversial view, it seems to me that these are quite possibly the most dangerous sorts of delusions.
I've recently run across this 2007 post on the blog Unqualified Reservations (archive best read here). It is written by Mencious Moldbug, who is probably familiar to some Overcoming Bias and Lesswrong readers. He is a erudite, controversial and most of all contrarian social critic and writer. In 2010 he debated Robin Hanson on the subject of Futarchy.
Violating Godwin's law to breach the fence between religion and ideology to see what cognitive dissonances we can dredge up is old hat for us LWers (A Parable On Obsolete Ideologies 2009 by Yvain).
I hope you can now see reason I've picked a partially misleading title, since I think Moldbug makes a pretty convincing argument that belief in "religion" may be considered harmful even for atheists, let alone those of us who aspire to refine rationality.
In such a model questions like "is the Church of Scientology a religion?" dissolve rapidly. Whether something should be tax exempt because it is "really" a "religion" or "a church" is a legal question of importance only to activists trying to challenge law and lawyers, that shouldn't change our ethical intuitions or cause us to try to imagine a sea or play up rather minor geographical features, to separate the continents of Religion and Ideology in our maps of reality.
Every single proposed mechanism for the retention and spread of religion from convenient curiosity stoppers, indoctrination of youth, to tribal identity markers hold for ideology just as strongly as for religion. Even seemingly very specific memetic adaptations like "God of the gaps", seem to arise in various non-theistic ideologies. Maybe similar adaptations arise because it is the same niche?
Thinking about the implications of such a hypothesis, atheism for one additional god is a rather easy step of rationality to take. Very few people believe in the great Juju or Zeus. Adding YHWH to the list isn't that much of a stretch, for those fortunate enough to be educated and living in most of the West.
But how hard is it for someone to question, in a unbiased fashion, such gods and holy words such as say Democracy?