This is not what the Buddha said to the Kalamas in Kesaputta, India (AN 3.65). But this is how he is commonly quoted.
Buddhism is a call to free inquiry. It is not a free for all, no rules, Zen hipster, polymorphous mess.
Believe something -- but what and why?
We are responsible for what we believe (think), what we understand (know), what we feel (experience as emotion) in response to things, and what we do (karma). It is all a re-action to something. And action is karma.
The Buddha clearly said that those decisions should not come from simply being told something, or because it is tradition, or because it is attributed to some authority.
Moreover, it should not be believed simply because it agrees with reason (which is based on our assumptions about reality). One should not simply buy into a theory one likes. That is no way to know. And what "common sense" would we resort to other than views we prefer?
The Buddha asked the Kalamas, What do you think: When greed, hate, or delusion arise, does it arise for one's own good? No, the Kalamas answered. Does it arise for the good of others? No. Does it arise for the good of both? No.
Therefore, the Buddha responded, since you know this to be true for yourselves, abandon it. You do not need an authority or prophet, a seer or scholar to tell you that. He went on to teach them, reminding them not to abdicate responsibility. We are responsible. Our advice?
- Go to primary sources: Read the sutra