If you don't have me you will face

Question

On many minds of the human race
If you do not have me you will face
Turning me high at a feeding place
Being considered a family disgrace

Hint (upon request)

Fast

Answer 1

Here's an answer:

HAIR

On many minds of the human race

literally above your mind on the top of your head. And a huge topic of fashion.

If you do not have me you will face

A pun. If you have no hair, we can see your entire face - not covered by a beard, moustache, locks, etc

Turning me high at a feeding place

Hair must be worn high if you are serving in a restaurant or fast food establishment

Being considered a family disgrace

Hair is often a source of drama, there have been high profile news stories lately about it especially in schools, but I believe what this is really getting at is a well known but unusual quotation:
"Does not nature itself teach you that if a man wears long hair it is a disgrace for him" - 1 Cor. 11:14 (and similarly women can experience similar disgraces if missing hair, e.g. v6 "But since it is disgraceful for a wife to cut off her hair or shave her head...")

Re hint:

Fast food (above) and it grows fast, especially when the barber shops were closed.