Much of our behaviour towards our offspring is dictated by cultural and social norms. In some cultures the application and displaying of tattoos is very important in every day life, showing one's status within society and marking the passing into adulthood. One could postulate thus that tattoos are something quite harmless and there would be nothing against the wish of parents desiring to have tattoos applied to their baby's skin in order to indicate their joy with their newborn and display this to the world. At a later age the child or adult could proudly display said tattoos as a sign of parental love and care.
After all, parents already determine the religious faith or lack thereof their child grows up with, what education they receive and what they are and aren't allowed to see, read and watch. What possible harm could there be in leaving a physical mark on a child's skin in addition to the life-long impressions left on the child's mind and psyche?
In Western society the answer to this is codified in so many child protection laws. No parent shall knowingly and willingly inflict physical or emotional harm onto their child, lest child protection services become involved, or even the justice system in severe cases. Tattoos are definitely a step too far here, as indicated by the outrage expressed by many at the sight of young, pre-teen girls being forced through the motions of a beauty contest, dressed up and with make-up applied to give them the apparently of women many times their own age. Clearly that's as far back as the line goes, and less far again in other Western societies.
One of the main issues which people in general have with inflicting permanent, physical changes to an newborn's body is that the newborn in question has never given permission, and secondly there is no appreciable benefit to such an action. One even has to consider the possibility of severe psychological trauma as a result of this choice as the newborn grows up into a child, teenager and adult. What will the impact be on the person's emotional health? How will one's environment handle it? Might it negatively affect the person's chances to get a good job, successful career and loving relationship?
In light of this the moral and often legal consensus is that it is fully amoral to apply a tattoo to a baby's skin or other individual incapable of making an informed, personal choice.
This does, however, lead to the interest conundrum that every day again in the same Western countries parents knowingly and wilfully consent to have their baby permanently and physically altered in a way which goes far beyond the impact of a mere tattoo, which one could reason is not that permanent any more with the host of methods to remove them these days. The victims of these surgical alterations are infants who have the misfortune of having been born without clearly distinguishable male or female genitals.
These surgeries have as goal to completely remove any trace of the 'wrong' genitals, while making the Chosen genitals look as normal as possible. Which side gets picked and as a result which physical sex and thus gender role gets assigned is done purely by chance, as there is no way to tell for an infant which physical sex or gender role they may prefer as they mature into teenagers, roughly twelve years later. The use of chromosomal tests to see which sex chromosomes (XX, XY, other) are present in the infant is meaningless, as made abundantly clear by the existence of transsexuals.
Salient point here is also that none of these so-called 'normalization' surgeries are medically required. In fact, they are dangerous, potentially harming or even killing the infant as full narcosis by infants is extremely risky. One must also question how many of the victims of these surgeries later identify as 'transsexual', unaware of their medical history, as all too often these normalization surgeries are neither recorded nor reported.
These leaves us at the rather awkward point where we can all share moral and ethical outrage at parents who would consider tattooing their baby or infant, yet who would at the same time jump at the chance to forever alter and scar the same infant with unknown consequences for no realistic gain. Because it's a sin to not be 'normal'? Just like 'everyone else', as if one can truly take a random group of individuals and split them strictly across a male/female line keeping in mind both biological characteristics and gender role preferences.
In some way this situation reflects the moral ambiguity and hypocrisy in society. Tattooing a baby is 'wrong' because it makes it less 'normal' and it wasn't a voluntary choice, but removing a half-formed uterus from an intersex infant's abdomen is perfectly okay, because it makes the infant more 'normal', even if it wasn't a voluntary choice.
Because who doesn't want to be normal?