I think King though was seen as more difficult because of her role in pushing the women's game, the development of professionalism, and gay rights forward. There is no doubt that she would be classified in the vernacular here as a 'nippy sweetie' but I see that as no bad thing.
The first two perhaps, but as I remember BJ was only associated with gay rights after an ex girlfriend "outed" her without BJ's consent. On the court (!) in the sixties she was seen as an aggressive player & a bad loser, obviously she was not and is not the only one.
The whole issue of the effect of someone's views and actions upon the honours paid to them for entirely unrelated matters is a mass of grey. There is no doubt in tennis terms that the naming of the arena is deserved and appropriate but there are many unrelated actions that someone could take outside of tennis that would mean such an honour would be changed instantaneously. That King thinks a boundary has been crossed here is not surprising. I suspect that the Oz tennis authorities are quietly hoping that as you have suggested it is something that they can postpone till Court dies, but that could easily be another 15 years or so away.
Margaret Court has expressed some views which may be unpopular, but they are not illegal. Twenty years ago, Gabriela Sabatini expressed similar, if more moderate, anti lesbian views, and she too would probably be vilified if she expressed the same today
