Mitchell Tace Chapman, 18, from Sunderland, was due in court but the Crown Prosecution Service has decided to discontinue the case.
A Northumbria Police spokesman said: "An investigation took place in relation to this case and the decision to charge was made.
"Following a review of the evidence by the Crown Prosecution Service (CPS), a decision was made not to proceed with the prosecution."
A CPS spokesman said: "The legal guidance for such offences is that a communication sent has to be more than offensive to be contrary to the criminal law.
"Even though the content expressed in the communication is in bad taste, controversial or unpopular, and may cause offence to individuals or a specific community, this is not in itself sufficient reason to engage the criminal law.
"While there is no doubt that the comments will have been deeply upsetting to the families and simply offensive, the threshold for proceeding with a criminal charge is very high.
"The question that prosecutors have to answer in this case is not whether the message was offensive, but whether it was so grossly offensive that criminal charges could be brought.
"In this case, the comments made do not meet the required threshold for a criminal prosecution and the CPS have advised the families and the police that the proceedings against Mr Chapman are to be discontinued."