But master can mean many different things other than “a white man owning black slaves in 19^th century US” – and was not created with this name in mind; whereas the sport team name was unambiguously chosen and featured a caricature of the very thing they chose their name after on their logo.

It's a 'caricature' in that choosing societies renown for being valiant warriors erases much complexity (how much nuance and complexity were you expecting from a sports mascot?). Anyway, if this were a sincere movement, it would similarly object to equivalent depictions of the Irish, Vikings, Romans, Spartans, Trojans, etc.

No, it's a caricature because I mistook the Cleveland Indians logo for the Washington Redskins logo, my bad.

I see your point, but even still no one objects to the Fighting Irish or Boston Celtics logos despite being every bit the caricature. Are we doing this out of respect for Native Americans, or is it to make ourselves feel noble while we (myself included) make no progress on their material concerns?

The whole "invaded their homeland and then slaughtered most of them" factor is certainly in play.

Are you being ironic or are you unaware of Irish history?

Many are woefully iggnorant of the trials of the Irish sadly.