Cherrybim, before you start to wonder why they would ask about hair covering before, for example lashon hara, tzedaka etc- it’s quite obvious why it’s often used to guage level of observance.
We can’t peer into people’s hearts and determine their level of emunah & bitachon. We can’t overhear their prayers and determine their level of kavana. And if we don’t know the woman personally we may not be able to figure out how pure her speech was or how much chessed she did without nosey yentish inquiries that would inevitably lead to lashon hara and rechilus being spoken. We certainly cannot ask about taharas hamishpacha, and even shemiras Shabbos can be shakey inside the daled amos of a person’s home without strangers being any wiser. Hair covering is there for all to see easily.
At least that’s how it was in the olden days. Some 21st century human hair sheitels may leave you wondering. But that’s a different topic for a different thread.