Real estate websites like Trulia, Zillow and others pay 3ard party vendors to copy property information from counties across the U.S. This includes property taxes. However, in a few states, property information is not public so it cannot be shown on websites. Not sure if your state is one of those non public states or counties.
As for realtors adding tax information to their listings, realtors do not want to take on the legal liability if the tax information is not correct. Therefore, as a buyer, your best method is to have a realtor email you listings directly from the MLS. All MLS systems in the U.S. provide the latest tax information for all homes for sale. In your situation, you will be better served getting listings directly from the MLS.