Here’s the history of this practice: The 1917 Code of Canon Law specifies that women are obligated to cover their heads when approaching the altar and whenever in the presence of the Blessed Sacrament. This tradition (as evidenced by St. Paul’s treatment of the topic) was part of the Christian Tradition since the earliest days of the Church.

Now, here’s where it gets tricky. In 1983, the Code of Canon Law (which replaces the 1917 Code) doesn’t mention this practice. At all.

So, here are the facts: Catholic women are no longer obligated to observe this practice much like all Catholics are no longer obligated to abstain from meat on Fridays. The practice is not null, but it is no longer obligatory. Just as we are all called to make some sort of sacrifice every Friday in memorial of the Passion (be it abstaining from meat, making an effort to spend extra time in prayer, giving the money we might spend on a fancy coffee to the homeless person we pass on our way to work, etc.), we (both women and men) are still called to discern how we can approach the Blessed Sacrament with special humility and reverence (be it wearing a veil, changing out of our gym clothes before coming to Mass, making the sign of the cross whenever we pass a church, etc.).

This is a decision that the Church has left to your prayerful discretion. If it makes you feel uncomfortable, don’t do it. Don’t feel obligated to do it. If you find it meaningful and empowering, well, then go ahead. Make sure you understand why you’re doing it and make sure you’re doing it for the right reasons.