Body typeface

Dear brothers and sisters in The Church of Jesus Christ of Latter-day Saints,
Can I tell you the fonts used in body text, not the logo?

It's called Ensign. It's not publicly available, but for many other non-latin alphabet languages (as well as monospaced text) the church uses Noto which is available at https://fonts.google.com/noto (and also has the standard latin characters)

Some variants of Baskerville and Open Sans are similar to the serif and sans-serif fonts used by the Church, and older publications (like the hymnal) use a variant of Palatino.