An enigma wrapped within a mystery
Wittgenstein had many close friends who were clearly Marxist, and one example of this was George Thomson. In fact Thomson thought Wittgenstein was a Marxist himself in practice just like himself.
Wittgenstein had little time for the depths of advanced capitalistic dictatorships, and hated the bourgeois life at stuffy Cambridge University. Towards the end of life his he gave away his wealth and supported the ideals of austerity as being good for the soul.
In fact in 1935, Wittgenstein travelled to the USSR during the times of Stalin, and even advertised that he'd like to become a Communist worker there. The Stalin officials were bamboozled by his strange kookiness.
Kulturkritik influences
Oswald Spengler was one of the most conservative thinkers of the 20th century was certainly one of Wittgenstein's greatest influencers. His German model of Kulturkritik, with its anger towards liberal values and equality, was also shared by Wittgenstein.
It's plain to see that Wittgenstein's political thoughts were a quagmire. He was never really a political thinker. He was rife with political contradictions, and very few of them could be linked to his philosophical genius.
As a pessimistic middle class conservative, Wittgenstein did not shun modernity, but also linked up with Communism to congratulate and to damn some of their philosophies.
At the end of the day Wittgenstein's philosophies are at best system smashers. Like Nietzsche, @mindhunter and @baah, we declare the overthrow of our idols to be a vital part of our task. With hammers in hand we have our best philosophical tool at hand. As Wittgenstein once stated: 'All philosophy looks to destroy its idols.'
And the search for Wittgenstein's own elusive politics goes on ....