These definitions come from Webster's Collegiate Dictionary fifth Edition copyright 1944. What is considered obsolete in this dictionary may not have necessarily been considered obsolete when the King James Bible was transcribed. The KJV Bible was originally transcribed and published before 1944. The obsolete definition may more than likely be the definition that was being used, since all verses are taken from KJV Bible.

Publican - [Of publicain, from late/low publicanus] 1. Roman Antiquity - A farmer of the public revenues; hence, a collector of toll. 2. British - Keeper of a public house.

Where it can be found in the Bible:
Matthew 5:46-47
Matthew 9:10-11