It also isn't a matter of belief. If you show me a grown parent that legitimately believes Santa will bring presents to their kids, they'll only be disappointed once. It's a marketing gimmick convenient for parents because it encourages good behaviour. It would be far more useful to not put them through the eventual trauma of realizing it later in life and instead focus on gifting gifts to each other in the spirit of some holiday because they care about each other. Instead we all play a stupid game that involves lying because we're too afraid to be the one who isn't.
What if another family is foreign, and has not such myth or custom? How does that child feel in an environment where the people teaching them are telling them their own parents are lying to them?
Respecting a belief is one thing. Pretending it is true is another.
The ideal thing to do would probably be to tell the teacher/school admin at the beginning of the year that the child knows Santa isn't real and have the teacher pull them aside before the class Xmas party and reaffirm that your kid is so super mature for knowing the truth but since the other kids aren't as grown up as they are, they've gotta keep the secret.
You can definitely not do Santa but also find out ways not to make parenting your kid's friends and classmates difficult (because if you do, other parents will avoid you and you hurt your kid socially!)
We give gifts to each other on other holidays, birthdays, and even for no reason at all. Isn't that a better thing to teach a child to comprehend than a made up sky person who sneaks in your house after dark and who is constantly watching what you do, even while you're asleep?