I am against a 6E at this time, but this is how I'd do the changes to account for modern social visions.
1.) Each PC would select a Humanoid Type, a Class, a Background, and a Profession.
2.) Humanoid type would provide you some purely physical characteristics tied to the form of the humanoid type. It would also give you points to spend in your background and profession. A race like aarakocra would get fewer points to spend elsewhere because it gains a power ability through the humanoid type.
3.) Class would be much as it is now, but would also include a bonus to the prime attribute of the class.
4.) Backgrounds would be much as they are now, but would you'd spend points from the pool provided by your humanoid type to obtain features from the background, like proficiencies, special abilities, tool proficiencies, etc... You would get an ability score bonus from your background choice.
5.) Your profession would be what you currently do as a newly heroic figure. While background looks at where you were, profession would look at where you are. Many of them would be tied directly to combat, but some options would focus on social or exploration abilities. Again, you could use points from your humanoid type to buy abilities in your profession. You would also get one ability score bonus from your profession. You'd be able to choose a second background as your profession, or something more focused on adventuring that was only available as a profession.
6.) If all three ability score bonuses (class, background and profession) are in the same attribute, you move one to an attribute of your choice.
7.) We'd establish that only humanoids have free will. Everything else, in the standard setting, is guided by directives put into them by the Gods or other forces. They have personalities, but they are programmed to be a certain way, and are not allowed to deviate without magic.
8.) However, these directives would not be alignments. Alignment would be removed from the game. Instead, these directives would be rules that the creatures without free will must follow and believe - and have no choice but to follow and believe. A red dragon would inherently value wealth, despise those weaker than it, and enjoy cruelty. You could shape the rest of their personality when one is met, but all red dragons would share the same core rules of belief and nature.
9.) As mentioned - no alignment. Instead, we'd focus on shared belief structures. Instead of a magic sword only being useful to good PCs, it would only be useful to one that was blessed by a certain deity. Instead of having spirit guardians dealing damage type based on alignment, it would be a choice.