I'd say that the key science that we on the left would seek to make free of theism is the science of human history, historical materialism. In that context , "materialism" is another term for atheism and science.
God and religious dogma are most problematic when believers force them into history and politics. ( See _ Socialism: Utopian and Scientific_ by Frederick Engels, for example, where Engels discusses philosophical idealism as synonymous with theism .)
This is more specifically problematic because the effective political agents of the ruling classes act and think as atheists, and by that get a strategic political advantage on oppressed class political agents who act based in theistic belief.
On the other hand, certain interpretations of God can produce effective political actors for oppressed classes - like John Brown, Harriet Tubman or Martin Luther King , jr. However, overthrowing capitalism probably can't be based in religious ideology.
I don't think belief in God necessarily messes up physics theorizing . Newton believed in God. I think Stephen Hawking is a believer.
As to biology, to the extent that some one is a creationist or intelligent designist, it will mess up their natural history theory, though a believer might suspend belief for practical biology , such as medicine
Charles