Those who say that science fits religion are arrogant for they mean their own religion. There are many faiths that oppose science - some even forbid going to the doctor. The rest feign devotion to science but prove by their actions that they oppose it. A fit would be a two-way thing. Science reaches to religion and religion reaches to science. It makes no sense for science to be asked to do theology.
Also religion that argues that hearsay is enough to justify belief even unto martyrdom, is clearly contradicting scientific methodology which can be summed up as, "Keep checking and let the evidence speak. Keep your biases out of it."
If religion says evil is not a thing but a defect, science has to assume it could be either for it has no way to test. For that reason, science weakens the notion that an all-good God who is not the maker of evil may exist.
And what about this? "Headaches getting better after aspirin do not mean the aspirin cures them though it could. The real cause is some unseen power in aspirin, a secret miracle." Miracles weaken the impact of scientific truth.