And that's another reason I don't root for ex-Tigers on other teams.
Big league baseball players are not my friends or family members. They are merely employees of an organization for whom I root to win games on the field. I know zero about most players personally. As such, I don't know what true colors they are going to reveal once they go to another team, but even if they do, that's not going to change what I feel about them personally, because I feel nothing about them personally, if that makes any sense.
When I root for a player on my team, I am rooting only for his effect on the team, not for the player personally. So if he does something objectionable as a Tiger, for example, keeping a second family, it doesn't affect how I root for him, because I'd been rooting only for his output, anyway. Would I rather have a good guy playing for my team than a bad guy? To the degree that it matters, which is minute, sure, why not. But that's only a nice-to-have, not a must-have. Beyond that, I have no personal stake in what kind of people these guys are off the field.
This is why I don't root for ex-Tigers on other teams. Because he's not a friend or family member, when he engages in something on another team like "bang a gong", I feel no betrayal or disappointment. He's someone else's problem now. Flip side, if he wins a Cy Young and a ring, I feel no joy, because he had to beat my team in order to get there.