In such an environment, increased intelligence (or similar mutations) or social structures/culture and technology would add no benefit. They would never be developed (further), the whole species would stagnate at that point.
I think there would still be evolution, but more in the sense that it follows a single track.
Many of us can blame (relatively to the topic at hand) conservative or reactionary positions all we want, but they do seem to fulfill a very useful role in getting others to question their beliefs (whether they want to or not). If only to build a better case for their beliefs, but often with the result of changing opinions. This is more on the human society scale, but it can include technology or anything else.
I think there's a lot that can happen to a society and/or species that is never threatened past a certain point. I think examples in Mass Effect include the Asari, who arranged and persist a system that is arguably best for them, but also great for many, so they feel comfortable about it, and never truly threatened (except in the most rare circumstance and fullest extent of Rachni and Krogan conflicts).
We saw what happened to them:
1)They enjoyed the fruits of peace, for many thousands of years (I think? Was it 1000s or 10,000s?). In this time, they could be seen as dominant over even the Turians (to an extent), and enabling of constant progress, even if that progress was of the more specific Asari way.
2)They suffered what may be viewed as the most brutal defeat of the war. At least the Batarians were utterly blindsided. At least the Humans are still resisting. At least the Turians are kicking ass. At least the Krogans never give up, ever. At least the Salarians are seemingly doing what they can to actively keep out of conflict as long as possible. But the Asari? Their system was about ready to burst and they still thought they would be okay (at least on the species cultural scale, of course).
I think stagnation is only if everyone involved follows ONLY ONE way. In this case, only things tied to that ONE WAY advance (even though it could be argued that in some societies, everything IS MADE to be tied to that ONE WAY, so it still advances). But I don't think that's the same thing as focusing on coexistence over survival. Coexistence isn't collectivism, though I think those are often mistaken.
In fact, there is always change happening. It just depends on what level, and if it is your type of change or not. A 'species' might hypothetically stagnate, but their technology or their influence or whatever else could still grow and change, albeit in a more specific way than it would if there were most competing voices within that species.