Why do people behave normally when they come across Ted

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"