There are many types of weird ideas. We have some categories here, but it is true that some ideas fit in more than one category:
We try to steer clear of religion and religious beliefs in this effort because for the most part these are not beliefs about nature - they are super-natural. Some religious beliefs do concern the natural world and thus are subject to scientific scrutiny (e.g. the age of the earth). Conflicts with these beliefs is inevitable and needs to be handled carefully. It is important to stick to the scientific evidence and what it shows and not attempt to critique any non-science evidence presented.
It is inappropriate for a public school teacher to be interrogating students' religious beliefs or dictating which beliefs are correct or incorrect. This would be a violation of the 1st Amendment.
For these reasons we do not delve into these conflicts as much as the other types of ideas. We simply note that these beliefs exist and should be kept outside the science classroom.