Question, I was told by a woman that they check women's underwear. If it is told that they weare thongs, or French cut panties, the priest may check. This woman's neighbor had an issue like that and had to go to the Big Church on the Beltway (495---that goes around DC)
It really just depends on your area. It's been my experience that Mormons - and I'm speaking primarily of the women - gossip more than any other church-going people. Even though Brigham Young spoke at length about the evils of gossip, it's a staple of Mormon life.
How does that relate to privacy issues?
Well, in some areas, the church is more invasive than in other places.
Some people will say, "At tithing settlement, the bishop asked whether I'm a full tithes payer and I told him I was."
Others will say, "For my temple recommend interview, my bishop said I'd need to bring in my previous year's tax return."
I've never personally experienced the tax return thing myself, nor do I know anyone who's ever been asked. As for those who've been raised in the church, however, I do know of someone who swears that her great-uncle(?) had to produce his tax returns in order to be eligible to advance in the church leadership past a certain level.
-----
In some places, two unmarried, Mormon adults can live together and no one will say a word. But in other areas, the gossip-mongers will make it their business to cause trouble and the next thing you know, the co-habitants are called in to see the bishop. The bishop, after speaking with the member(s), will then determine whether he needs to call a bishop's council or even a stake disciplinary council.
FYI:
ward = single church group, determined by geographical boundaries, and the bishop is the presiding official over a ward
stake = group of wards, also determined by geography, and the stake president presides over the stake
stake high council = 12 men called to assist the stake presidency
--------
Based on the arguments presented, the stake presidency could then decide to disfellowship (shun) or even to ex-communicate the members. If disfellowshipped, the person would be restricted from going to the temple, holding a 'calling' (church job), taking the sacrament, and could even be restricted from bearing their testimony.
Although not common, this stuff can and does happen in the 21st century.