It is, however, missing a piece: why are there people who don't share all five foundations?

You are right that Haidt is missing that piece, although judging by his recent writings, he might be slowly converging towards the answer. Namely, the answer is that, contrary to Haidt's model of contemporary ideologies, there are in fact no such people.

What does exist are people whose ideology says that harm and (maybe) fairness are the only rational and reasonable moral foundations, while the other ones are only due to ignorance, stupidity, backwardness, malice, etc. Nevertheless, these same people have their own strong norms of sacredness, purity, authority, and in-group loyalty, for which they however invent ideologically motivated rationalizations in terms of harm and fairness. These rationalizations are usually very flimsy, and often they amount to little more than an instinctive emotional urge to dismiss anyone who asks unpleasant questions as crazy or malicious. Yet, given the high status and institutional dominance of such ideologies, their adherents generally do manage to create a public image of themselves as concerned only with the "rational" foundations (and thus superior intellectually and morally to their ideological opponents).

As for the claim that "you need loyalty, authority and sanctity to run a decent society," I would actually go further and say that they are necessary for any sort of organized human society. In fact, the claim can be stated even more strongly: since humans are social beings who can live and reproduce only within organized societies, these things simply will exist wherever there are humans. Therefore, if you are concerned with harm, the only reasonable question you can ask is about the practical consequences of the (necessarily multi-foundational) social norms in different societies on whatever metric you use to evaluate harm. And here you will find that, even in terms of a purely utilitarian metric, an accurate analysis of the social role of the norms based on these "irrational" foundations will give you very different answers from those given by the pseudo-rational ideologies that claim to reject these foundations.