In terms of issues of the Avengers' diversity, I think of Avengers Vol. 3, #27. This was a time when the line up was changing for a number of reasons. In previous issues, protestors were outside Avengers Mansion proclaiming that the team either didn't have enough minority members or too many mutant members. (Later issues would reveal that this was the Triune Understanding, the Avengers' enemy at the time who were inciting the protests). The Avengers acquiesced to such demands, but it definitely led to conflicts amongst the team and their government liasons. Here's what happened when such a liason, Duane Freeman, calculated the benefits and costs of letting go mutant members of the team:
Tony makes it very clear that Avengers membership is about getting the job done. It's open to anyone who can get that job done. As it always has been, whether that's been to Black, Hispanic, the gods, whomever. At the same time, Tony questions. Could the Avengers be unconsciously choosing white members? Tony hates to think he is, but maybe. I appreciate this scene. Good intentions are there, but maybe that's not enough. And members self-reflect, and ask themselves maybe they aren't doing the right thing. The whole issue in itself is a good read. Indeed, after reading it recently, I realized just how relevant it was to today's issues. Yes, people got angry over prejudices, inclusion, exclusion, all of that. But people questioned themselves. Maybe their beliefs weren't a hundred percent correct. Indeed, if those beliefs were true, then how come characters felt wrong afterwards?
Regarding the female characters, Peter Sanderson, Marvel Comic historian wrote how the Avengers' female characters just pointed and commented on things for many years (a la Scarlet Witch), which was in contrast to the X-Men's female characters. Reading more X-Men stories recently, I've noticed that. The X-Men's female characters really took center stage in a number of stories. Still, the Avengers have had women play prominent roles. Wasp, Black Widow, Scarlet Witch, Captain Marvel (both Carol and Monica), and many others, they have been in several high positions throughout their tenures as Avengers.
As an aside, I think that another reason why the Avengers were not as popular as the X-Men also came down to stakes. Reading X-Men stories, I'm noticing they're constantly attacked. They're under threat every, single time,. Like damn!
In short, the Avengers have done much in terms of diversity. However, there's still room for more to be done.