[After the war, he did start the KKK but the Klan that he started, didn't target blacks as much but carpetbaggers and that Klan was abolished.]
Source?  Wikipedia seems to indicate to the otherwise.
"in the August 1867 state elections the Klan was relatively restrained in its actions. White Americans who made up the KKK hoped to persuade black voters that a return to their prewar state of bondage was in their best interest. Forrest assisted in maintaining order. It was after these efforts failed that Klan violence and intimidation escalated and became widespread.[62] Author Andrew Ward, however, writes, "In the spring of 1867, Forrest and his dragoons launched a campaign of midnight parades; 'ghost' masquerades; and 'whipping' and even 'killing Negro voters and white Republicans, to scare blacks off voting and running for office."  He gave Order No. 1 to abolish the KKK but by that time they were spread throughout the US.  The article does agree Forrest evolved by the end.