Exactly, I watched the Ken Burns special on Jack Johnson back when it was broadcast and it was pretty obvious Johnson got shafted by the feds because he was a famous, rich, black guy that not only dated white women, but did it flamboyantly. A big no-no in those days. If I remember correctly, the feds actual created a law just so they could convict him, it was something about forbidding a black to transport a white across state lines, for sexual purposes. That being said, I not sure what it accomplishes nearly a century after the fact, when everybody involved is dead and the best you can hope for is to waste a lot of money and resources for what will be a little more than a footnote in the history books.
Nope. He was prosecuted for transporting a woman across state lines for "immoral purposes," under the Mann Act, which does not mention color or race. Still a law, I believe, though seldom used.
Since he wasn't married to the woman in question, there is no doubt he was guilty. There is also no question the prosecution was racially motivated.