Clive and Sacha are both right to criticise Dawkins' lack of understanding as to why people are religious and his non-materialist approach that ignores its social basis.
But to answer Joe's points:
1. "marxists are not pure materialists and Marx himself argued against such people."
Marx argued against some materialists on the grounds that they had not fully broken with idealism (the idea that abstract concepts such as 'justice', 'truth' etc are not socially formed but are eternal and predate human consciousness) which as he points out ultimately leads backs to believing in the existence of God and others for not applying dialectics to materialism but none on the grounds that they were "pure materialists".
2. "I think private belief in God is compatible with Marxism. As I understand it Jim Larkin was a catholic yet was on the executive of the Communist International, and I'm sure there are many other examples."
Clearly it follows that belief in God is not compatible with Marxism and the example you cite is one of personal contradiction. I am sure you are right that there are many more. I also think the CI was correct to allow someone who was a genuine workers' leader and a practicing Catholic onto its executive, whatever his lack of grasp of Marxist philosophy or inability to apply it in his personal life. The AWL - and other Trotskyist groups - have had Christian members in the past. As long as they accept the discipline of the organisation and are not a proselytiser for religion (i.e. a priest or similar) it isn't a problem. But their philosophical views are not Marxist.