Moral realism I take to be broadly the view that moral judgements can be true or false, that some are true and are known to be true. There has been an upsurge of interest in and sympathy with moral realism among philosophers since roughly the mid-1970s. I account for this on three grounds :
▻ the decline of empiricism
▻ the phenomenology of the moral life
▻ the dominance or rights discourse
The decline of empiricism
In the mid-1930s in the analytical tradition logical positivism, a radical form of empiricism, presented a straightforward challenge to moral realism. Moral judgements were deemed to be incapable of verification and hence to be 'meaningless'. Still the fact of moral judgement needed to be accounted for; and the logical positivists relegated moral judgements to the mere role of expressing and eliciting emotion. This is the theme of the famous or notorious chapter 6 of AJ Ayer's Language, Truth and Logic (1936). The emotive theory of ethics, barely sketched by Ayer, was developed with some sophistication by Charles Stevenson in Ethics and Language (1944).
Emotivism never achieved an entirely satisfactory formulation, not least because it did not have an adequate philosophy of language.
The early 1950s saw the emergence of RM Hare's prescriptivism in The Language of Morals (1952). Hare elevated moral judgements above the status of being merely emotive but did not entertain the idea that any moral judgement could be actually true.
Logical positivism proved an untenable position. Hare's prescriptivism ran into difficulties, mainly because it allowed just anything to count as a moral judgement provided certain formal conditions were met.
Moreover, empiricism, which provided the main backdrop to the critique of moral realism, was seen to be holed by serious difficulties - the myth of the given and the theory-ladenness of observation were powerful tools of critique of empiricism. Quine's 'Two Dogmas of Empiricism' (1951) also assailed empiricism as traditionally understood to devastating effect.
A major prop of empiricism, employed against moral realism, also suffered major assaults - this was the correspondence theory of truth. If moral judgements are true (at least some of them) then they must correspond to (moral) facts or states of affairs but how could such facts or states of affairs be detected or recognised ? Indeed, what could they possibly be like ? 'The cat is on the mat' is true (if it is true) because it corresponds to the perceivable real-world state of affairs of the cat sitting on the mat. What would a real-world moral fact or state of affairs - the wrongness of saturation bombing of a civilian population, say - be like and how could one perceive its presence ? We could perceive the bombing but how could we perceive its wrongness ?
The correspondence theory of truth ran into great technical difficulties, and found rivals in deflationism and other theories.
All this meant, as some philosophers realised, that the tools used against moral realism - logical positivism, the emotive theory of ethics, empiricism and the correspondence theory of truth - had nothing like the cogency they had once been widely thought to possess. Therefore moral realism was again an option. Eager interest ensued and moral realism turned out to be, whether or not the correct stance in ethics, capable of serious defence. It naturally therefore attracted followers. I am doubtful about whether moral realism is the majority view in professional philosophy but it certainly has numerous and adept defenders.
The phenomenology of the moral life
If we reject moral realism then we apparently have to deny that it is true that the Shoah was evil, that it is true that the holocaust in Rwanda was a shameful tragedy of unjustifiable violence, that it is true that torturing other humans or sentient creatures for fun is wrong, and so on and on. Moral realism appears to many the strongest and perhaps the only barrier against moral scepticism, subjectivism, and relativism all of which (it is widely supposed) fail to deliver the truth that certain actions and states of affairs are purely and without qualification as a matter of fact wrong. This is definitely how some experience the moral life - as a life in which it must be true that certain things are wrong. Moral realism speaks to that mindset.
The mindset is not new, of course. But 24/7 media news coverage, instant global communication, the opening of archives, and many other factors have brought moral catastrophes vividly home to us as never before. The mindset has been reinforced, and moral realism is the beneficiary.
The dominance of rights discourse
The language of natural or human rights is of longstanding. In political discourse it goes back at least to the American and the French Revolutions in the 18th century; and it has an even longer philosophical history. I will mention only Locke's Second Treatise of Civil Government (1689). In more recent times the Universal Declaration of Human Rights made its appearance in 1948.
None the less rights-talk entered a new phase in political and moral discourse in the United States and Western Europe from the 1970s. It is now the, or a, dominant mode of discourse. The case for abortion, for instance, is commonly couched in terms of a woman's right to control the condition of her own body. Claimants of this right do not, so it seems to me, regard it as anything other than true that they have it. They do not claim it as one might express a wish or vent an emotion; they claim it as a moral fact or truth that they have this right. If this is not the case with all claimants, it is so with very many.
Or if we consider the issue of gay rights, there we find the right to same-sex marriage widely demanded, when it is demanded, as a moral entitlement of a factual kind. It is true (not just a subjective opinion or an expression of Western values) that gaylife is an equally valid lifestyle; it is true that gays should have the right of same-sex marriage : this is the prevailing sense of campaigners's arguments.
I am simply characterising the discourse; my own views cannot be inferred about abortion or same-sex marriage.
It seems to me that the logic of universal human rights requires the invocation of truth, hence of moral realism. What would one have thought if the Universal Declaration of Human Rights had ended with : 'Of course it isn't actually true that we have these rights but they are something we support' ?
My own views about moral realism are of no relevance here. I have simply tried to answer the question and to explain why moral realism is on an upswing.