It is said that when Ganesha was travelling on his mooshika vahana (the mouse vehicle) with a big belly after a heavy lunch, the mouse toppled over and Ganesha fell down. It was a night lit up by a gorgeous Moon (Chandra). Looking at the scene below, the proud Moon couldn't contain his laughter and burst out cackling. Ganesha felt insulted and in a fit of rage cursed Moon to loose his charming beauty. But after much coaxing by the entire pantheon of gods, Ganesha watered down his curse. He said that whoever looks at the Moon on the Bhadrapada Chaturthi (the day on which Ganesha chaturthi is celebrated; i.e., today), he/she will be a victim of vicious and false accusations for the entire next year. So Hindus usually avoid looking at Moon on this day.
Coincidentally, today is also finale of Ramzan (Ramadan). For Muslims the festivities of Qutb-e-Ramzan, after the month long fasting during Ramzan, is heralded by looking at the faint crescent of Moon. So until and unless they look at the infant Moon, they will not partake in festivities.
So, today at one side you have Hindus who are deliberately shunning a glance at the cursed Moon while on the other side you have Muslims celebrating the vision of a delicate Crescent. This is the irony of faith.