Even though you cited v15, I don’t see your counter to my last point. I can still appropriately repeat myself, this isn’t reason to detract from Paul’s comment “her glory” and instead to imply he really meant “care less”. Of course on your point we can agree, it has no bearing on salvation, but it still doesn’t detract. Are you insisting it does? It can’t if it isn’t related.
Verse 15 isn’t in the same context as verses 3, 4 and 5. The “careless” is about hair covering or uncovering in verses 3, 4 and 5. Where he is concerned with hair then there is concern about hair. Verse 6 and beyond is about how a woman covers her man/husband and the hair is an example and a play on words with head in verse 3 and head, body part.

1 Corinthians 11:3 But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God.
1 Corinthians 11:4 Every man praying or prophesying, having his head covered, dishonoureth his head.
1 Corinthians 11:5 But every woman that prayeth or prophesieth with her head uncovered dishonoureth her head: for that is even all one as if she were shaven.
1 Corinthians 11:6 For if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered.