I could say pretty much as Dawkins says, namely "having voted Left all my life", when I've voted in Oz (not sure I would now, but that's another matter. I'm in Hong Kong, so for the duration am not obliged to vote in Oz).
But as to Dawkins wondering "why" the Left supports Islamism, there are books on this. I have three in my Library: Unholy Alliance, by David Horowitz; United in Hate, by Jamie Glazov; and The Third Reich and the Ivory Tower, by Stephen Norwood.
The last title is interesting as it chronicles the cheerleading in the 1930s by US universities of Hitler's burgeoning Nazi party. Given the similarities of fascism with Islamism -- "Islamofascism" it has been called -- we now have the same cozying up of the Left with the fascist right. Again. When after the war all right-thinking people said it should be "never again".
I think the primary reason for "why" is that the Left is reflexively anti-American, as are Islamists. For the Left it's Amerika; for the Islamists it's The Great Satan. (*)
This visceral hatred of the free-market, individualistic, capitalist Superpower -- so much at odds with socialism's collectivist, statist leanings -- trumps the Left's concerns, such as they are, with their other "ideals": freedoms of speech and conscience, support for women's and minority rights and so on.
I guess that Dawkins' parenthetic "Islamism is not Islam" is pre-emptive protection against predictable attacks on him that not all Islam is extremist (only a "tiny minority" are!...)
However, there are plenty of powerful arguments that Islam (not just "Islamism") is at its core violent, and that its doctrinal Trinity are all texts that counsel violence.
Indeed the Turkish Prime Minister has said there is no moderate and non-moderate Islam. "Islam is Islam" says Erdogan. Quite.
Even if you accept the distinction between Islamism and Islam and assuming that by "Islamism" you mean its violent wings, it bears repeating: that there's an awful lot of violence done in its name, considering it is supposed to be "a tiny minority". This "tiny minority" is daily killing scores of people. In the last few days, nearly 100 in Kenya (specifically non-Muslims, ie, the Kufar) and in Pakistan around 80 Christians slaughtered in their Church. Just two days, in the work of the "tiny minority" of Muslims who have, we are assured "misunderstood" Islam. Awful lot of misunderstanders aren't there? (The Religionofpeace.com has been keeping a daily tally since 911. It's now up to nearly 22,000)
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(*) LATER: A thorough report from Mariam Namazi's One Law For All report, "Siding with the Oppressor, the Pro-Islamist Left". Extract:This damning report exposes their [the Left] agenda and methods, including the use of accusations of racism and Islamophobia and their conflation of Muslim with Islamist in order to defend Islamism (which they see as anti-imperialist force) and Islam (which they view as an oppressed religion) rather than out of any real concern for prejudice against Muslims or the rights of ‘Muslims’ who are incidentally the first victims of Islamism. Challenging this perspective is especially important given its wide acceptance as ‘progressive’ in mainstream society. [my emphasis]
