In a closed primary state, one must declare their party allegiance before given a ballot. That is designed to prevent democrats from diluting the republican race (and vica-versa) by voting for the RINO/Moderate (read wimpy, spineless) candidate.
Tennessee is an open primary state, so democRATS routinely invade the republican primary to get the RINO onto the regular ballot.
He declared himself a republican solely to choose the less conservative candidate in the primary. He donated to blue.
That’s my understanding.