For TOS:Considering the degree of gender inequality against the feminine still prevalent in our culture, male and female cast members should be inverted-- so the ensemble is female dominated. Kirk, Spock and McCoy would all be women, and Uhura would be the only man.
To be further socially relevant, the characters of Chekov and Uhura should have a contemporary equivalent: Instead of Russian, Chekov would be Arabic—and accordingly renamed (America’s so-called national enemy); Uhura would be Hispanic – and renamed (America’s racially disenfranchised).
Female Scotty would still be Scottish and female Sulu would still be Oriental Asian.
Female Spock would be someone with exotic appearance, and female McCoy would be older than other human command crew. Someone in the crew needs to be homosexual.
To depict the current status of equality black people have attained in our society, female Kirk would be Black; might be paradoxically small in bodily stature, but big and Shatner-esque in personality.
To accommodate new names for the Chekov and Uhura characters, everyone could be re-named, but keep the same character traits as originals.
AND every nationality played by an actor of that nationality; i.e.- Scottish woman playing Scotty.
For TNG:Again, gender reversal; i.e.- female Picard/ male Dr. Crusher/ female Wesley.
Riker would be the female version of a ladies man, commenting on the sexual double standard.
Nationalities are completely open for all human characters, except Caucasian would be in the minority.
Also, HUMANS must be minority. This, of course, would necessitate re-naming all characters, while maintaining original character traits. Instead of being blind, female Geordi should be a “little person”.
Male Troi would still be alien-human hybrid, but not necessarily Betazoid. Female Worf may be represented by different alien.
Data would be a robot instead of android, and less human looking.
At least one minor crew member needs to be homosexual. This and an Andorian character would well facilitate commentary on sexuality and gender identity. Given the generally mainstream status homosexuality has attained, hermaphrodite should be the new gay-- someone in the command crew.
AND every nationality would be played by an actor of that nationality. i.e.- a Frenchman played by a French actress.