he Nazi Party’s 1920 “Twenty-Five Point Program” demanded:
"…that the State shall make it its primary duty to provide a livelihood for its citizens… the abolition of all incomes unearned by work… the ruthless confiscation of all war profits… the nationalization of all businesses which have been formed into corporations… profit-sharing in large enterprises… extensive development of insurance for old-age… land reform suitable to our national requirements ..."
Yes fascism and anarchy are completely opposite, anarchism allows anything to happen. There are no laws and no regulations. If you want to mix with a nigger, you can. You want to burn down someone's house? No problem because there is no police force. You want to kill someone? Go ahead because there are no laws preventing you from doing so. Anarchism is always right-wing because how can business be controlled if there is no central government?
Fascism on the other hand is different. You want to set up a business? You can if it doesn't damage the well being of the people. for example if you want to start a pornography company you wouldn't be allowed, because the government says it isn't right. This makes fascism left win, because it takes some control over the economy.
Of course you can be left-wing and ant-racism, like communism for example. In the USSR everyone was seen as equal. That is the fundamental difference between national socialism and communism, even though they are both left wing, one of them is ethnocentist (nat soc) while the other is cultural Marxist (communism)