For my own part, it seems to me that when I do that, my behavior is in large part motivated by the belief that it's good to avoid strong emotional responses to events, which is just as much a moral belief as any other.

There are situations where emotions need to be temporarily suppressed -- it needn't involve a moral belief. Getting angry could simply be unhelpful at that moment so you suppress it. To do so, you don't need to believe that its inherently wrong to express strong emotions.

That particular moral would come with its disadvantages. If someone close to you dies, it is healthier to express your sorrow than avoid it. Some people don't change their behavior unless you express anger.

Many think that morality is necessary to control the evil impulses of humans, as if its removal would mean we'd all suddenly start randomly killing each other. Far from saving us from suffering, I'm inclined to think moral beliefs have actually caused much suffering: for example, some religious belief is evil, some political belief is evil, some ethnic group is evil.