Ted is famous and most of the people will be aware that a walking talking teddy bear exists in the world but its not normal to come across a walking talking teddy bear in daily life at a public place. It is strange that people are not even excited to see him. Why is that so?
Its not normal to come across a walking talking teddy bear in daily life at a public place
It's not normal in our reality but it is normal in this movie universe
As Wikipedia says*
In 1985, 8-year-old John Bennett is a lonely child living in Norwood, Massachusetts, a suburb of Boston, who wished for his new Christmas gift—a jumbo teddy bear named Ted—to come to life and become his friend. The wish coincides with a shooting star and comes true; word spread and Ted was briefly a celebrity.
Ted has been around for over 25 years and his existence is well known. Certainly he's unique and one could argue that he should be more of a celebrity but people get blase about such things.
* Thanks to @BCdotWEB
In fact, as noted by @Gallifreyan it's stated that
"Eventually, nobody gives a shit"