Does the finding that the Earth circles the Sun challenge some incorrect religious dogma? Sure it does. Does this mean that one cannot teach this evidence without taking a “religious” stance, or adopting a “godless worldview”? Of course not. Religious beliefs are completely tangential to the evidence that the Earth circles the Sun rather than the reverse as many religions once taught.
Of course some seem incapable of noting this distinction. Just because a finding challenges dogmatic religious belief doesn't mean the Scientist has taken a stance either for or against that religious belief. The evidence is what it is.
Even the Pope believes in the weight of the evidence. So teaching the evidence is taking a religious stance for the Pope and against Young Earth Creationists? No. Teaching the evidence is teaching the evidence. That is Science.
When all you have is a hammer problems look like nails.
While the facts of science are neutral the framework in which they are taught are not, and it is impossible to teach in an environment free of framework.
There are only 2 possible options:
1) Science can reflect the glory of God and the facts presented within that framework. This is not religiously neutral in content or consequences.
Or...
2) Science and its facts are presented in a framework that ignores God. This is not religiously neutral in content or consequences.
There are no other options.
Please, let's get government out of the K-12 religiously non-neutral education business. Let parents and teachers decide upon a godless or God-centered framework in the private setting of private schools.