Aristotle already points out in his Metaphysics that some philosophers took chance to be a cause. So in the very early thinking on physics chance wasn't ruled out as a cause.
InIt was ruled out in the modern era it wasdue to the success of Newtonian Mechanics that installed strict determinism as a principle of Nature and this was principally due to the influence of Laplace. However there were dissenters, for example in the book Philosophy & Physics, its pointed that Antonin Cournot, the 19thC19th C French mathematician and economist, stated that chance ought to be considered as a cause in physical thinking. This view was of course vindicated in the early 20C when chance was discovered in physics - radioactive decay and then more fundamentally in QM.
This dethroning of Newtonian determinism had its dissenters , most prominently by Einstein. However he found the loss of locality in QM far more problematic. Given that General relativity was the culmination of a long search since Newton for local theories of physics, which was first achieved in electromagnetism and then gravity - this is not so surprising.
I don't see how taking chance to be a cause is problematic for either Islam or Christanity. As in both, the physical world is ruled by Gods law in the world which is then merely seen as physical law, and chance as a cause is nonetheless ruled by physical law.