Traditionally, women have been expected to wear hats (or some type of head covering) in Christian churches. Yet men (except officiants) are required to remove any headgear. Why is this so?

Hats for women is based on a passage written by St Paul in 1 Corinthians 11:5-15. Since it is being read in English, after having been written in Greek, there is a lot of discussion about the real intention of the passage!

https://lifehopeandtruth.com/relationships/family/role-of-women/must-women-wear-hats-at-church/

This passage from the NIV shows two different wording to describe the intent of the writer.
https://www.biblegateway.com/passage/?search=1%20Corinthians%2011%3A5-15&version=NIV

The situation for men is related to differentiating Christian worship rituals from those of the pagan religions around them, in which head covering was expected.
https://entrustedtothedirt.com/2020/06/08/whats-up-with-the-male-head-coverings-in-corinth/