Whether Hindenberg personally hated Hitler is immaterial. He and the entire monarchist conservative right never once saw the Nazis as "socialists". They never thought the Nazis were "left wing". They were the most powerful party of the right, which is why Hindenberg allied with them. And why the Italian monarchy saw the fascisti as allies.
People who consider the fascists, "socialist", ignore where they came from. The roots of fascism were not in Marxism. They were in the elite raider units that were formed in WW1 to raid opposing trenches. In Germany they were called stormtroops and in Italy Arditi. Mussolini was an Arditi. The "socialism" of fascism was just trying to transpose "band of brother" comradeship of an elite assault unit on the nation at large.
Under fascism, the traditonal power centers of the conservative right (Big Business, the Army High Command, the aristocracy, High Society, the Italian monarchy, the traditional churches, etc) survived intact. The power centers of the left were completely destroyed. The right survived so well, that the old boy network was the base for the anti-Hitler plot.
RE: He and the entire monarchist conservative right never once saw the Nazis as "socialists". They never thought the Nazis were "left wing".
A big error on the parts of monarchists and true rightists. Although, mostly, I think they feared Hitler. Hitler could whip the crowd into a fury, and true rightists (such as me) view unruly crowds as a threat.
Mussolini actually had been a socialist. So his roots very definitely were "on the left."
But the controversy is a little silly. Nazism and Fascism were syntheses of "right" and "left" ideas of the day, and it's hard now to unsort out the mixed elements and put such movements firmly on one side or the other.
In the context of the 1920s and 1930s -- international communism defined as the "left" and street fighting between National Socialists or Fascists and Communists -- one can make a case that Hitler and Mussolini were more right than left, but that only goes so far, and you miss a lot if you try to pigeonhole their movements according to a right-left schema.
Conservatives were more scared of the Bolsheviks (can't say I would have blamed them) and they saw Hitler as the best way to keep Germany from it. They thought they could control Hitler, and then he would fade quickly. They were dead wrong. Sometimes the enemy of your enemy is still your enemy.