It's fascinating that you're really not supposed to talk about this stuff, much less analyze it. So... let's analyze it.
It's interesting that we accept the significant cultural diversity added to the OT Rebellion but would likely not accept it in the OT Empire (though interestingly, diversity was clearly evident in the First Order in TFA.) I mean it's a Galaxy far far away so anything should go, right? But obviously in the OT, we're in WWII. The Rebels are symbolically the Allies, and the Empire symbolically is the Nazis - obviously in ideologies but made specific by costume. The Rebels are "us" - the good guys, the Allies/Alliance.
But if you take that approach it gets tricky... pretty much all the allied forces were white male, certainly 100% in leadership roles from all Allied nations, and for most of the war all Allied nations firmly resisted allowing people of color to serve - with some notable exceptions, but usually when they were in a serious manpower pinch and had no choice (and often "colonial forces.") But surprisingly on the other side the Nazis, despite their evil racist ideology, fully accepted the non-white Japanese as their Axis allies, and for example sheltered Muslim leaders who were enemies of the British and trained Muslim soldiers to fight in the German Army.
So overall ideologies aside (and the Imperial British ideology of the time was more than a little questionable,) in terms of diversity, it's uncomfortable to see that the Nazis and the Allies were actually probably more equal than you'd believe.
After all, the British - the lead nation of the Allies and most significantly the basis for SW's Rebellion in terms of costume - were just as much a racist "Imperial Empire" (invading/occupying, colonizing, brutalizing people of color etc.) at the time of WWII as the Imperial Empire in SW. Perhaps this is why all Imperial officers MUST have a British accent.
So the Empire in SW is an interesting thematic symbol - and part of that construct is clearly race, "whiteness" and the ghosts of a racist past - even if it is pretty divorced from the social realities of the WWII era (even at home.) And it's interesting to see how 2010's era sensibilities have stepped in to tweak the in-universe reality presented in the OT. A common approach in movies is modern sensibilities applied to the past, so maybe that's part of it.
What people forget is that ANH WAS controversial even in 1977 for its no-diversity cast and they are clearly tweaking that to how it should have been (though it could be argued that an all-white cast thematically reflects the truth of WWII being an all-white affair, just shifted to space,) but the actual "rules" they've used to do that are uncomfortable to discuss, because it touches raw nerves of what's going on politically across the Western World - and even in Hollywood itself.
From RO Yavin to SW Yavin? Not for me when watching them back to back. The skeleton crew at the beginning of the movie when Jyn was interrogated was pretty much all white (Cassian notwithstanding but we know why HE wasn't in ANH, lol.) Leaders of other ethnicities (like Bail and the rest) seemed to come and go only when an important meeting was to take place.
It is what it is given the wildly different times each film was made and I think they're doing as good a job as they can with working in more diversity into the existing saga.
What I notice most in terms of the two Yavin bases (besides diversity I mean) is the lack of shower and laundry facilities in the RO base. Sweat and stubble clearly ended as a trend the week before ANH begins.
I like to think the Rebellion opened its doors to Skid Row that week and by the following week when ANH starts, everyone was all scrubbed up, clothes laundered and stubble either shaved or grown into full beards.
