That’s why I cited an objective, historical definition of leftism: so that I can say that no, the people you’re talking about are not leftists, because they don’t fit this definition. They may call themselves leftists, but that doesn’t make it so, any more than Hitler calling himself a socialist, Stalin calling himself a communist, or North Korea calling itself a democratic people’s republic makes it so.
The same goes for religion, by the way. Thumping the Bible doesn’t make you a Christian. Loving thy neighbor does.