If I call myself a Scotsman, despite not meeting the definition of a Scotsman (never been to Scotland, have no Scottish heritage) then it would be fair to call me not a “True Scotsman.”
If the definition of “Christian” is “someone who follows the teachings of Jesus” then someone who spreads hate does not meet that definition.
If the definition of “Christian” is “anyone who calls themselves a Christian” then the definition is so broad it is useless as a descriptor. It includes someone who is loving and caring, and someone who abuses and murders anyone they disagree with. It tells you nothing about the individual or how they behave.