Should words be capitalized for being religious terms?

While googling about whether "atheist" should be capitalized, and skimming past posts by people blogging about atheism rather than about English grammar, I came across http://uwf.edu/writelab/reviews/capitalization/

It says

[Capitalize] Religions and religious terms

Examples:

Catholicism, Hinduism, Buddha, the Bible, Christian, the Ten Commandments, Baptist church, Mt. Zion Methodist Church

NOTE: Do not capitalize the following:

Examples:

church, communion, atheist, agnostic, spirituality

but I don't recall hearing of such a prescription before. Wouldn't most of the examples listed be capitalized because they're proper nouns? Are there good examples of words being capitalized solely because they're religious terms?

I'm mainly interested in modern English, rather than days of past where a lot more words were capitalized than they are nowadays.

Somewhat related: When should the word "God" be capitalized? - use "God" when referring to the name of the god of Judaism and Christianity (a proper noun), but "god" when referring to the general concept of a deity (common noun).

Should words be capitalized for being religious terms?

Not necessarily. It depends on whether they’re considered proper names.

For example, church, communion, atheist, agnostic, and spirituality are not proper names because they’re not recognised entities.

In contrast, the Church of England is a proper name because it refers to an institution and should therefore be capitalised. However the church is not capitalised when you’re simply referring to a building rather than to the institution itself.

Holy Communion should be capitalised as a proper name; however, communion used as a general term should not be, because it isn’t a proper name.