In some established, mostly Catholic, Christian societies; infant baptism has been the norm, and baptism regarded as essential to salvation - and performed as an emergency by anybody at hand if an infant was about to die.
Yet in some devout Protestant churches, baptism is something that happens (if it happens) mostly in teenage or adulthood, and is therefore implicitly regarded as optional to salvation.
Catholic baptism makes sociological sense in that, in an already-existing Christian society, pretty much everybody is brought up a Christian unless they opt-out.
People in such societies are not 'born again' because they have never known anything different - they are swimming in a sea of Christianity, do not need specific instruction in Christianity - it is all that they have ever known.
Thus baptism is not about choice, but a normal practice - a necessity, but also very preliminary to the real business of a Christian life.
(In such societies, the most highly religious people adopt the religious life (monasticism), and seek to become Saints.)
When baptism is of infants, and near universal, and linked with salvation; the fate of the unbaptized infant becomes a major theological concern and problem - with various proposed solutions, such as Limbo.
By contrast, in some Protestant societies, baptism is a matter for adults, and is therefore an opt-in.
The background assumption seems to be that people will not be Christian unless they specifically choose to become a Christian.
The religious life is conversion focused, and the convert is born-again very explicitly. There is much need for teaching, since one cannot assume that the average citizen knows what it means to be Christian.
Since baptism is not quick, or universal, and is not of young children; then the specific Catholic concern over the salvation of infants is not prominent.
(e.g. Devout English Puritan reformers of the Book of Common prayer wanted to stamp-out the practice of emergency baptism by midwives - the implicit attitude being that it was better for infants to die unbaptized than for such practices to encourage the wrong attitude to baptism.)
Infant baptism, and baptism generally, is therefore one of the major differences between (sincere, devout, real) Catholic and Protestant Christians.
My only observation is that the general attitude concerning children throughout the New Testament seems to suggest that the salvation of children is not a problem.
This is not a matter of theology, but a matter of what is suggested by the stories, and what is left-out of the theology, or is ambiguous or unclear.
There seems to be an implicit background assumption that (young) children are innocent in practice (leaving aside the aspect of original sin) - and the salvific concern is with adults able to comprehend and choose.
This could imply that the eternal fate of children is so bound-up with, assimilated-to, that of adults (parents) such that no separate treatment of the matter is possible; or that children have 'different rules' including a free pass of some sort - perhaps that sin is an 'adult' phenomenon (with a borderline between child and adult that is necessarily imprecise).
This line of argument tends to support the Protestant theology, however it does not invalidate the Catholic practice of infant baptism.
On the one had it supports the Protestant idea that infant baptism is not necessary to salvation; on the other hand it does not support the (sometimes) Protestant idea that infant baptism is wrong, invalid, and should be prohibited.
I must admit that, although I personally was baptised as an infant and not by immersion in the Catholic-Protestant Church of England, I find it hard (in my simple-minded way) to understand why it is that adult baptism by immersion as depicted so prominently and explicitly in the New Testament has become so unusual among the major Christian denominations.
Leaving aside the consequences of not doing it; it just seems very obvious that when Baptism is done, it would be done in the manner of the New Testament accounts.
I'm not saying that differences from NT baptism practice have any particular bad consequences - at any rate, I don't see this in church history, not clearly; but I find it genuinely hard to comprehend why baptism would be changed, on the basic principle that if a church fundamentally changes baptism practice (given that baptism is so obvious and fundamental to the conversion process in the NT) then what would not be open to change?