The Bible prohibits tattoos. (Leviticus 19:28). I'm sure the athlete you describe means well, but it's still prohibited if he is in fact Jewish. He was likely mistaken or unaware. (Alternatively, a non-Jew could choose to express solidarity with the Jewish people by obtaining a Jewish star tattoo, if it floats his boat; that really doesn't do anything one way or the other. The tattoo prohibition is only for Jews.)
There is some discussion whether only symbols, words, and the like are prohibited; or even things like permanent makeup or artificial dark spots used in reconstructive surgery; but the Jewish star is a symbol and thus definitely prohibited.
The Talmud actually does one better -- what if I tattoo upon myself: "I am for G-d"? Or "I belong to G-d"? Still prohibited.
As Rabbi S.R. Hirsch explained (in his Bible commentary, Frankfurt, mid-1800s), the only permanent mark we inflict on our bodies is circumcision for men, as required by the Torah. For us to permanently mark ourselves with any other image implies an allegiance to something other than G-d. Okay, so why not tattoo yourself with "I follow G-d"? Because that implies it was a personal choice up for you to make!