The Danes and the Dutch don't need mandatory helmet laws because they have a bicycle culture. "I never saw the cyclist standing at the stop sign," in the automobile-centred jurisdictions will get the motorist who killed or maimed a cyclist off with commisserations from the magistrate for his sleepless nights; in The Netherlands he'll be facing a manslaughter charge and have to prove he took every precaution not to run over a cyclist. It's a fundamental shift in the onus of proof that translates to wideranging differences in road behavior.
In the jurisdictions with a bicycle culture they cycle slower anyway than eg Americans do; Americans who commute are the inheritors of a road-racing culture that started with the Peugeot 10-speed in the 1970, and one often finds American commuters making ludicrous statements about a cyclist's "duty" of keeping up with traffic, meaning automobile traffic. The British commuting ethos, such as it is, too derives from road racing, and aims at fast transits. The Dutch commute at 15kph, a recent study found. Add that difference to the cycling culture enforced on automobilists (who are very likely in other parts of their lives to be cyclist too), and the requirement for a helmet appears in a totally different perspective. It would very likely be counterproductive to force the Dutch to wear cycling helmets, as the inconvenience to routine bicycle users of carrying a helmet into their daily affairs could drive many of them onto other forms of transport. (This is the same argument as the one for not forcing people riding metro rental bikes to wear helmets.)
That just scratches the differences, but I can't resist adding that according to a Dutch friend with 7 or 8 bikes I wish he would send me (just saying!), the Dutch anyway wear helmets already whenever the occasion calls for it, which he defines as being on his road bike, especially training at night, or riding offroad in icy conditions; his photographs show that his mates do the same.
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I'm not at all impressed by claims that mandatory helmet laws keep anyone from cycling. Those who want to commute will find a way to deal with the helmet. Those who will benefit most from the helmet, the casual cyclists, will either cycle or they won't, and the helmet has very little to do with it. As for putting kids off cycling by a helmet requirement, so what? If they won't wear the helmet, it is better for them not to be on a bike on the streets. The only place where there is a sound argument against helmets, is in pick-up-here-leave-there metro rental bike, where you really can't expect people to lug around a helmet on the offchance of wanting to rent a bike, and the hygiene implications of publicly shared helmets are shudder-making.
The question really isn't whether mandatory cycling laws will keep anyone from cycling (if they won't wear the seatbelt, we don't want them driving because they're likely to do it in an antisocial manner; the argument for helmets is the same), but whether they're necessary and/or where they are necessary.
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In fact, mandatory helmet laws are altogether a distraction, a bodge. The true question is whether any particular society wants to be an automobile culture or a bicycle culture, or, more practically in most, whether it wants bicycles on its roads at all, and how it proposes to share the space.
