First, to directly address the (not exactly identical) question in the title:
Does the Origin of Religious Beliefs from Evolution cast doubt on Christian belief?
No, because from a Christian perspective, the very premise is flawed. We must start by asking whether this assertion has any credence, since a faulty assertion has little power to cast doubt.
So, let's do that:
[Evolutionism claims that religion comes into existence, not on any truth claim, but from evolution giving us useful, but otherwise untrue beliefs.]
What is the proper response to this argument?
I'd be tempted to respond by systematically dismantling Evolutionism, which, after all, has essentially zero evidence. Unlike Natural Selection, which is the variation of what we presently call "species" within their created kinds, making use of genetic potential which they possessed at Creation and are slowly but surely losing (according to the laws of entropy/thermodynamics, i.e. The Curse), the entire argument for Evolutionism rests on the Naturalist' dogmatic rejection of God. Evolutionism is born not out of evidence, but out of invocation of the Holmesian Fallacy.
There is, in fact, significant evidence against Evolutionism. The lack of evidence is evidence in itself. The absurd improbabilities against it are evidence. Indications that life was designed (including some that are hillariously claimed as evidence for Evolution) are evidence against it. The lack of fossil corroboration, and indeed the failure of the fossil record to align with the philosophy, is evidence. The abject failure of the philosophy to substantiate its claims, and the number of times it has had to be revised as a result, is evidence against it.
I could go on — indeed, many books have been written on the subject — but we'd be here all week.
All this, however, is irrelevant, because 2 Thessalonians 2:10b-11 tells us "they refused to love the truth and so be saved. 11 Therefore God sends them a strong delusion, so that they may believe what is false". After reading this, I realized I need to be more phlegmatic about trying to argue with Evolutionists. They are wedded to their dogmas to a degree that cannot be called other than religious zealotry. "[Naturalism] is absolute, for [the Naturalist] cannot allow a Divine Foot in the door" (Richard Lewontin¹, evolutionary biologist). Their philosophy (might as well call it a "religion"; the distinction is academic) is predicated on the (unscientific!) a priori rejection of even the possibility of God existing, and for the very good reason that they recognize that, should they allow for said possibility, the evidence in favor of it is nearly overwhelming. In the words of Romans 1:20, "His invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made."
The important take-away here is that the claim in question comes from this same philosophy; namely, that Naturalists will believe anything, no matter how absurd, to avoid confronting the possibility that God actually exists.
Therefore, I suggest what may seem a rather odd approach: preach the Law and Gospel. If someone is not completely lost to the Truth, the power of God's Word and the mountains of evidence in favor of the same (and, yes, in favor of Creation) will reach them. Show them that God's Word is true, and that it is Truth. If they are lost in their delusion, as per 2 Thessalonians, no amount of arguing or evidence will reach them. (Indeed, the ability of Naturalists to ignore inconvenient facts is astonishing.)
(¹ I've also seem assertions that Lewontin himself is not making this claim, but rather observing that it occurs. For our purposes, the latter is still sufficient; it does not matter what particular individual is operating in this manner, but that Naturalists as a whole tend to operate thusly.)
As an aside, I'm amused by the claim that 'religion gives us useful beliefs'. The evidence for (traditional) religions, particularly Christianity, providing for a better society is all around us. One needs only to compare the early USA to its sad state today, or to Marxist countries, to see that clearly. The implication therefore that an Evolutionist would somehow find Marxism "better" is... interesting.
This, of course, leads to a counterpoint with respect to religion being "useful". Christians clearly ought to (and do) argue for the societal value of Christianity. From our perspective, of course, God gave us religion — say, more specifically, the Law — because He knows our nature, and knows the sort of messes we humans devolve into without that guidance. Moreover, the Bible tells us that we were Created with a conscience, and that evidence of Creation is all around us (n.b. Romans 1:20 again). Thus, the case for the existence of religion, even among those that don't know Christ, is quite clear when approached from a Christian starting point.