Based on Iris Murdoch's essay "Morality and Religion," should morality follow rigid rules like the Ten Commandments, or is there a more flexible alternative?

Murdoch is responding in the third paragraph to issues around moral complexity, such as the difference between duty and virtue. Murdoch associates "duty" with "orderliness"; in a morally ambiguous world, rules are needed to preserve humans from self destruction. They provide a much-needed simplification. She talks about different moral "styles," which we must navigate between as we balance different obligations. They cause one to "have to choose between being two different kinds of person." Murdoch's discussion here of how the pursuit of virtue can lead to different "selves" is very compelling.

Tempting though it may be to use religious precepts or "duty" to simplify moral conduct, Murdoch argues that there should be "time off" from the demands of duty, but "no time off from the demands of good." She admits that the decline of religious absolutism in the West has resulted in an increase of happiness, albeit at the cost of moral certainty.

I can't speak to your own opinion of these matters, but Murdoch's writing here suggests a particular conception of the individual as someone who naturally tends to free thought. That is, the choice to embrace a moral code is an individual one; because it is a choice, even the decision to adhere to "rules" is a kind of moral relativism.

Does Murdoch suggest in "Morality and Religion" that morality should follow rigid rules like the Ten Commandments or allow for flexibility?

Iris Murdoch observed that in the nineteenth century, even writers who disagreed with the prevailing notion of morality based on divine command lived within it, as a fish swims through water. In the twentieth century, however, all moral systems appear contingent and flexible. This appearance of flexibility may be a question of rules existing in a hierarchy, with minor rules which can be broken when they conflict with more major rules. However, it may also be indicative of an approach to morality based on values.

It is clear that many elements of Christian theology conflict with some of the most widely-held values of the modern era, including those laid down in the Ten Commandments. Few people particularly care about the first four commandments, for instance. As for the tenth commandment, it would probably be regarded by most modern-minded people as immoral in several different ways.

You shall not covet your neighbor's house; you shall not covet your neighbor's wife, nor his male servant, nor his female servant, nor his ox, nor his ass, nor anything that is your neighbor's.

In the first place, this commandment treats women as possessions in exactly the same way as livestock. In the second place, it judges people for thoughts over which they have no control. In the third place, one might well argue that wanting what others have is a good thing, since this desire motivates hard work and productivity. Such an approach involves applying one’s values (equality, fairness, industry) to the rules. This renders the rules superfluous so long as the values themselves are strong and clear, since these values can be applied directly to any moral issue.