For example, Gould did (and Dawkins still does) engage in research into dysteleology -- the doctrine of purposelessness in nature. In fact, both have gone on record saying that, based on the evidence of "purposelessness" in natural structures (as supposedly manifested by the existence of vestigial or nonfunctional organs or parts), that God is either evil, stupid, or simply non-existent.
Surely "dysteleology" is attempting to find evidence against teleology in nature, rather than evidence against god. For example if you believe in a God without a plan or purpose in the natural world, then evidence against teleology doesn't amount to evidence against God. But if you believe in God's plan for the natural world, then evidence against teleology is evidence against your belief.
So it isn't that Dawkins disproves the existence of God. He is trying to disprove teleology, and whether you see that as a challenge to your religious beliefs just depends on what your beliefs happen to be. Dawkins has a problem with the major world religions, which all happen to have a purposeful God, so he is correct to say that evidence against teleology is also evidence against this conception of God. But that is just a logical consequence of the results of his research. It is not THE result of his research. The results of dysteleological research are that vestigial parts are nonfunctional, etc.