sassy, I'm not sure that I really buy the theory that Richard Duke of York wasn't the father of Edward IV. Nor am I convinced that he would order a low key celebration, even if it was true, on that account.
I mean did he say to his wife something along the lines of: "Yes, I will allow this archer's son to be my heir and inherit all my estates and even possibly the crown of England. But just to show how pissed off I am about you being unfaithful and foisting a bastard on me, we're not going to town on the christening, OK"?
I think that there were political reasons as to why George's birth was celebrated in a marked manner. At that point the King was still without an heir but York now had three sons and was arguably the most important noble in the country. One might have expected him to be an important figure at court, instead he had been sidelined by being sent to Ireland. It's a possibility that the fanfare was the DoY making a statement to the King.
There were always rumours that powerful men hadn't actually fathered their children - there was a very persistent one concerning John of Gaunt, for example. It was a neat way of undermining an enemy; in the same way as women were labelled whores or witches at the drop of a hat.
In a society where land meant power and primogeniture was all, an accusation of illegitimacy was just a way of striking at a family or an individual in order to weaken them. There didn't have to be any evidence, nor even any truth in the accusation.