Yes, moral codes encourage people to embrace suffering in themselves or towards others.

The argument

Morality can lead to more suffering than it relieves because some moral codes allow for the embrace of suffering in oneself as well as in others. It begins with the concept of moral certainty, which is the idea that something is probable enough to be considered, without any reasonable doubt, true. Once applied to morality, this often leads to the idea that this one morality is a universal truth. This idea becomes dangerous when two moralities of this same caliber meet. For when they do, the resulting disagreement can generate suffering on account of being rival interpretations. Take the Crusades as a historical example. The clash between Christianity and Islam resulted from each side having a perceived claim to the holy land. One can make the case that each side's sense of morality allowed them to press on fighting despite the number of people that would die from those incursions. That because both sides felt entitled to that land, they could keep sending soldiers out to die trying to acquire it, doing whatever they needed to do regardless of the cost. In a way, one might say their morality serves to justify their actions, resulting in needless suffering. Additionally, one can make the case that concepts such as utilitarianism also endorse suffering. Utilitarianism is a moral code whose ultimate goal is to maximize well-being. Sometimes this means that sacrificing an individual for the sake of a group is necessary. In the case of the train trolley redirect scenario, a utilitarian would endorse killing one person for the sake of five other people. Despite having the best intentions, utilitarianism still causes suffering because it still endorses suffering.

Premises

Counter-arguments

Conversely, not all moral codes embrace suffering but instead work towards easing suffering. For instance, Christianity lends itself towards humanitarian efforts. These efforts can come in many forms, one of which is advocacy. One instance that supports this idea is when the archbishop of York spoke out against cutting overseas aid in the UK, saying that they had both a social and moral obligation to aid in eradicating the unnecessary suffering of other people. The case shows that in advocating for the maintenance of international aid, the moral code held by the archbishop works to ease suffering as opposed to embracing it.

Rejecting the premises

[Rejecting P1] Moral certainty is a feature of some moral positions, not of morality as such. Scepticism, pluralism and fallibilism are moral positions too, and each cuts against the escalation described. The Crusades also underdetermine the case: territorial, dynastic and commercial interests are standard historical explanations alongside religious claim, so the example does not isolate morality as the operative cause. [Rejecting P2] Utilitarian aggregation is constructed to minimise suffering overall, and that it can license harm in particular cases is the standard objection raised against it from within moral philosophy — which is itself moral reasoning working to constrain harm. Treating one contested theory as representative of morality assumes the conclusion. [Rejecting P3] "Routinely" requires a comparison the argument never attempts. Prohibitions on killing, torture and cruelty, obligations of charity and hospitality, hospitals, famine relief and the campaigns against slavery are equally products of moral codes. The conclusion needs suffering caused to be weighed against suffering relieved, and only one side of that ledger is presented.