It is necessary to draw a slight difference between the two theories, in terms of International Relations and how they apply to the question of US nuclear policy
We'll start by talking about realism or realistic theory. When we look at the world and the mosaic of countries and territories into which it is divided, in addition to the more than 7,500 million inhabitants that exist on Earth, we perceive a first step variables that help to formulate explanations. The second step is taken by the changing scenario to be analyzed. Realism proposes an overcoming of both axioms, resulting in one of the theory with more pull. We could cite as references to authors as Thucydides, Machiavelli, Herny Kissinger, Hans Morgenthau, Robert Gilpin or George Kennan, to cite a few examples.
As a realist, the theory establishes the principle that all countries share a common space that could be called the "international system", and in which one characteristic stands out above all: the eternal struggle for power. Each country will act in accordance with its own interests, in order to maintain its autonomous capacity and guarantee the needs of the population it hosts. Since states are composed of human beings and power is a determining element in their persecution for the human psyche, this would be reflected in the foreign policies of states and in the way they guarantee it through force, which would include nuclear power, since conflicts in the world for realism are logical and constant, as a consequence of man's natural essence. It also explains the realism that power is never distributed in a fair way, rather those who possess it the most and are in a position to impose it will be the ones who occupy the most by subtracting the sphere of power from other States, although diplomacy is aimed at minimizing conflicts between States, and once again nuclear policy will be an asset that will be put on the table to achieve objectives.
The other pillar of US foreign policy, roughly and fundamentally, is idealism, which is precisely the theory that presents the most opposition to realism. The idealistic theory is based on the assertion that all States constitute a single international community, in which the functioning among them must be guided by the axis of the ideals of humanity and must pursue benefits for the entire community, with moral values and human goodwill being the nourishing substance of the functioning of the international community. As in realistic theory, the part is extrapolated through the whole, constituting an individual as the basis for establishing the community; the State. But a new criterion of centrality is established on which to base foreign relations, and that is that States should be judged as an individual is judged. So conscience plays a fundamental role in directing foreign policy and States will have to act in accordance with the good of all and the use of reason. The key is that the means are as important as the end, not the end that justifies the means. For idealism, wars in the common structure, the international community, are largely the consequence of the selfish acts of individuals who hold power, suffering the populations who have to bear it. In order to control these impulses, international laws and institutions are proposed that must be based on ethics. To cite some authors, one could start from Immanuel Kant, to synthesize, and in the case of the United States, the Fourteen points of President Woodrow Wilson, who also promoted the idea of the League of Nations, would be paradigmatic in this aspect. Precisely, Edward Hallett Carr was the one who promoted the term "idealist" to describe this line of thought from realistic positions in his work The Twenty Years Crisis, 1919-1939.
The question of nuclear policy
The current view of idealism about the consequences for humanity of a war of a nuclear nature is surely correct and pertinent, due to the risks involved in the use of these weapons, even if tactical, because of the proliferation that their use could entail a conflict, and the use by one of the contenders of a strategic weapon of these characteristics, which would mean a race towards madness or MAD (Mutual Assured Destruction). But the argument in favour of nuclear disarmament on the part of all players is the answer and that in this way the strategy of nuclear deterrence must be reduced necessarily implies a complete transformation of the way the inter-state system acts, which presupposes a forced time to try.
In this sense the oasis described by Francis Fukuyama in The End of History that encouraged optimistic post-Cold War positions affecting nuclear policy has dissipated, and with it the possibility of an early degradation of the nuclear deterrence strategy as a possibility of overcoming it would lead to its own failure in itself and involuntarily.
Idealistic thinking has tried to establish proposals promoted from the academic sphere to change the form of international relations and thereby steer nuclear nations towards disarmament. The United States has lived between the dichotomy of idealistic declarations and intentions and realistic practice, due to its position in the post-World War II world and the Cold War itself, which would lead us back to the dilemma of Poundstone's prisoner, game theory and John von Neumann with strategies based on Nash's balance, which has already been discussed. Keith B. Payne's article Realism, Idealism, Deterrence, and Disarmament is very interesting to read about this subject because it establishes a parallelism with a situation that qualifies, with great success from my point of view, to a moment of "waiting for Godot", since the arguments of idealists and realists about nuclear disarmament and that nuclear deterrence must be degraded makes one think of the characters in Beckett's work.
 It is evident that we are faced with an approach of 1+1=0 or zero sum, following John von Neumann, and again the strategies elaborated from Nash's equilibrium.
 Theatrical work within the genres of absurd theatre and Tragicomedy, by Samuel Beckett where the vagabonds Vladimir (or Didi) and Estragon (or Gogo) await Godot's never produced arrival by a road, producing conversations between the two, and even discussions. Irremediably, every day, towards the end, a character called Pozzo makes his entrance into the scene to devour a chicken and throw bones to both vagabonds, talk to them about George Berkeley's theories and make them dance to a boy called Lucky, who always ends up saying that he brings a message from Godot: "apparently, he won't come today, but he will come tomorrow afternoon". The end of the work is resounding:
Vladimir: Alors on y va?
Ils ne bougent pas.
PAYNE, Keith B., Realism, Idealism, Deterrence, and Disarmament, Strategic Studies Quaterly Fall 2019, 7-37. SEE: https://www.airuniversity.af.edu/Portals/10/SSQ/documents/Volume-13_Issue-3/Payne.pdf
POUNDSTONE, William, The Prisoner's Dilemma. John von Neumann, The Game Theory and the Bomb. Alliance 2015.