Yeats wrote "The Second Coming" as a response to the atmosphere of the postwar Europe. How are the anxieties expressed in the poem similar to those that might have been felt during and after wartime?

Yeats had a rather strange, esoteric idea of historical change. In very broad terms, he believed that history developed in a specific pattern which he visualized according to gyres or spirals. Each gyre represents a specific historical era, lasting roughly 2,000 years, and has its own unique set of characteristics. One gyre would be characterized by order and stability, only then to give way to another one marked by chaos and upheaval. In its turn, the new gyre would eventually vacate the stage of history, and order would prevail once more. 
Although rather unusual, Yeats's idea is not completely alien to us. When most people think about history, they have a particular shape in mind that they use to represent change, whether it is a straight line or maybe a circle. Yeats is simply using a different shape to help us understand his unique theory of history.
When Yeats wrote "The Second Coming" in 1919, much of Europe was in the throes of economic recession, disorder, and violent revolution. We do not have to look very far in the poem to pick up oblique references to the prevailing situation:

Turning and turning in the widening gyre.

The spiral of the old epoch of history is widening, and, as such, is ready to turn into another one. The existing gyre is associated with the birth, rise, and establishment of Christianity. It has brought some measure of order and stability to the world, but now its course has almost run. The gyre is about to change into the next historical cycle, one of a radically different, and more disturbing, nature:

Things fall apart; the centre cannot hold; 
Mere anarchy is loosed upon the world, 
The blood-dimmed tide is loosed, and everywhere   
The ceremony of innocence is drowned;

In the aftermath of the First World War, many of the old certainties had gone. Several royal houses had fallen; revolutions and armed uprisings were breaking out, and the very foundations of society appeared to be crumbling.


The best lack all conviction, while the worst   
Are full of passionate intensity.



Yeats was an unabashed elitist with a profound distrust for democracy. He tended to idolize (and idealize) the governing classes of Europe, especially the old families of the Protestant ascendancy in Ireland, many of whom he knew personally. In Ireland, as elsewhere in Europe, the postwar period brought about a decline in the political power of the aristocracy. In its place came a variety of mass movements, some of them democratic, while others, like fascism and communism, were considerably less so. In any case, Yeats and those who thought like him were deeply disturbed by what they saw as the rise to prominence of "mob rule," which threatened the aristocratic order they so venerated and cherished.
 
However, there is little that can be done about it. The change from one historical epoch to the next is inevitable. It will be a "Second Coming," alright, but it will be absolutely nothing like the return of Christ:


Somewhere in sands of the desert   
A shape with lion body and the head of a man,   
A gaze blank and pitiless as the sun,   
Is moving its slow thighs"



We do not know exactly what will replace our dying epoch. However, it will not be very pleasant, that much is certain; in the Bible, the desert is traditionally the home of the devil. Any creature emerging from there is likely to bring great evil with it. The bloodshed and chaos tearing large swathes of Europe apart is bad enough as it is, but much worse is to come:




And what rough beast, its hour come round at last,   
Slouches towards Bethlehem to be born?



The outgoing gyre was heralded by the birth of Christ. The one about to descend upon us has an altogether darker provenance. Though not intended as an exact prophecy of the tragic events of the 1930s and beyond, Yeats's apocalyptic vision still resonates due to the terrible fate that ultimately emerged out of the arid desert of postwar life and slouched its way towards Bethlehem.
https://www.poetryfoundation.org/poems/43290/the-second-coming