I am not a rude person I am thoughtful but I have ,forgot to RSVP to a childs party a few times.
definitively rude, sorry and very unkind. It doesn't matter if you receive 5 invitations a week: you open the letter, check your calendar ,and reply yes or no immediately. How hard can it be?
If parents think you are coming, they won't be able to invite someone else instead, they are paying and you are taking a space.
If everybody does the same, the birthday kid ends up with no one there. Would you like this to happen to your own child?
If the entire class declines a birthday party organised for my child, I cancel it and organise something else! As long as you know, you manage.
There are enough last minute issues, sick bug or other.
It's actually really rude and arrogant to think that it's only a birthday party, not a wedding. Some parents have saved a lot of money to be able to have at least ONE party for their kids, and it's a really big deal for them.
There are no excuse for not RSVP when you have received the invitation, none at all. Just text no and you are done.