We are thinking about getting a baby carrier. Our child is one month old. All of the carriers require his neck to be vertical, though the head is protected from moving side to side. The grandparents are saying that the baby's neck can't be vertical for a while and it's common knowledge. We know that his head needs to be protected from moving side to side because he doesn't have control yet. But if the carrier secures the head, is it ok if his neck is vertical? Grandparents are saying the head is too heavy and puts pressure on the bottom of the neck. But all baby carriers are designed this way. You would think the manufacturers thought about the neck vertical issue.
Women have been carrying newborns in a cloth wrap/sling since about... forever. Carriers are virtually modified slings, with some added safety measures.
Both are deemed safe. Especially if you use them for only limited amount of time and from time to time, which is probably the case.
Investing in a carrying device is a good choice - it allows you freedom of movement without a stroller and most babies love being close to a parent's body.
With regard to the grandparents' concern, if the head doesn't "flop around" when you move, you should be fine. If you carry your child in your arms, you probably do so in a (semi-)upright position anyway - or will soon, many babies prefer being carried upright. Then the head, while putting some pressure on the spine usually is supported by leaning against your chest or shoulder.
Yet not all carriers are created equal - before you select one, do some research on proper hip, back and neck support. For very small and fragile babies, some carriers are "too large" to support them properly.
If you want to be able to carry a baby (semi-) horizontally, no standard carrier will offer you this option. Slings, on the other hand, can be tied in a way that the baby can be worn in a horizontal position as early as day one. Like carriers, slings come in different qualities, especially the length, stiffness/elasticity ratio and quality of materials are essential. I suggest you check out the products of Didymos1, they are even used for premature babies in neonatal clinics. And, if this calms your grandparents, these babies are carried upright as well, see the picture here (text in German, sorry).
1 I have no affiliation with this company, I'm only a happy customer.
I don't know what kind of carrier you had in mind, but these are definitely safe from 1 month onwards: http://www.babycentre.co.uk/a559735/buying-a-sling-or-front-carrier