Regarding head coverings in 1 Corinthians 11: are Christian women supposed to cover their heads when they worship/pray? Is it a sin not to? Why did we stop this practice? It seems clear that Paul is referring to a head covering on top of long hair (long hair is not a substitute for a covering). It also does not seem to be a cultural thing, since Roman women in Corinth did not cover their heads. (It was a Christian thing.) Verse 16 says, "If anyone wants to be contentious [argue] about this, we have no other practice - nor do the churches of God." Does this not mean that God's true church partakes in this head covering practice? And that if Corinth did not do this also, they were not a part of the true church? I am scared to pray/worship now, since I do not want to sin deliberately.
You do not need to worry about praying and worshiping with your head uncovered. In 1 Corinthians 11:16, a verse you cited, the apostle Paul identifies the head coverings of the Christian women in Corinth as a “practice” or custom. A local practice or custom is far different from a universal principle from God, binding all women of all time to do the same. Because the Bible limits the instruction of head coverings to the women of Corinth in the first century by calling this a “practice,” women of other places and times are not bound to that instruction.
What was going on in Corinth? In the everyday, pagan culture of Corinth, women had head coverings (and you notice from the footnote in the NIV that such coverings could have been long hair in general or actual coverings to the head), recognizing by nature what God says in his Word—that men and women have distinctive callings in life as head and helper. The directive in 1 Corinthians 11 was that the Christian women in Corinth not to be social renegades, but living examples of biblical principles regarding men and women (1 Corinthians 11:3). By mirroring cultural practices that were occasioned by the natural knowledge of God and conscience, the Christian women of Corinth could reinforce that knowledge and display their faith so others could be positively influenced (Matthew 5:16).
I encourage you to recognize the Christian freedom you have when it comes to praying to God and worshiping him, and then exercise it with a clear conscience.