Again:
1 Corinthians 11:7-9 KJV
For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man. [8] For the man is not of the woman; but the woman of the man. [9] Neither was the man created for the woman; but the woman for the man.
Paul says a man ought not to cover his head (when praying or prophesying). He gives the reason. That reason has nothing whatsoever to do with "local custom" or "cultural practices". Instead, the reason is that the man is the image and glory of God.
The man is the image and glory of God in 1 century Corinth, and the man is still the image and glory of God in 21st century Texas. Therefore, the man ought not to cover his head in 1st century Corinth, and he still ought not to cover his head in 21st century Texas.
The same applies to the woman. Paul asserts "but the woman is the glory of the man". He states WHY this is so: "the man is not of the woman, but the woman of the man, neither was the man created for the woman, but the woman for the man." Those reasons were true in 1st century Corinth, and they are true today in 21st century Texas, Florida, England, The Country Formerly Known As Rhodesia, and Hong Kong, and everywhere else. Therefore, the woman ought to be covered when praying and prophesying then, and there, as well as now, and here.
Paul tell us us WHY the man ought to be uncovered, and WHY the woman ought to be covered. We have the reasons. We do not need to search for other reasons, because the Bible flatly tells us exactly WHY. And those reasons have nothing to do with social customs or cultural norms, but are based on how God created the man and the woman and thus what the man and the woman represent in a liturgical (spiritual) sense.
Since the reasons are still valid, the commanded practice is still valid.