Saying people deserve some equality of rights isn't saying they're 'exactly the same'.
There are two points relevant here:
1. There are different cultures, experiences, 'groups'. That's part of 'diversity'.
2. There is a history of some groups discriminating against other groups. Sometimes that involves 'race' as with the US history; or, nationality or other dividing lines, such as the history with some asian races such as Japan and others; or, there's the case of India's caste system history, and many others. The US experience has also included that, such as with anti-Irish prejudice for a period.
That sort of group conflict is different than 'different eye color'. There has never been a situation where a group of some eye color has discriminated against another eye color.
So, an argument to justify equal rights is that 'skin color is no justification for unequal rights any more than eye color'.
But that's not to say that 'diversity' is the same between different cultural groups and different eye colors.
Diversity includes both reducing discrimination, and benefitting from there not being people left out of things for no good reason but prejudice/bigotry/legacy racism etc.