For a simple good vs bad system, I'd definitely lean towards pushing it into mechanics. Pokemon has Return and Frustration, which deal damage based on how high or low your relationship with that pokemon is. You could have "Justice Strike" and "Backstab" for a similar feel. You could have certain characters and shops only available if you are good vs bad. There's also the question of if being "neutral' and/or "unknown" is useful or if the character should hard lean one way.
However, the idea I like for a morality system lines up with "reputation", where certain acts modify the relationship with other npcs based on their personal ethics and morals. It helps with characterization because it shows you what
they think a hero is or what
they think is the right or correct actions to take. This will in turn affect conversations, party choices, affect dual techs, etc.
In Skyrim (and likely a lot of other games) reputation is applied per region (city, faction, whatever works for the game).
Observable actions affect reputation. Good reputation in an area is generally optimal, especially since it gets you in good standing with the people in charge. Bad reputation can turn into bounties or otherwise make people eventually attack you. One cool upside here is that looting corpses isn't illegal but stealing is; kill someone, take what you want, then go to jail to get rid of the penalties, and you keep your "stolen" gear.
villainous actions decrease your rep and heroic actions
What you define as each of those sets a tone for the game, and how you get villainy or heroism to go up matters a lot. For instance, look at how wonky Fallout 3's system is; You can walk into a bar, shoot someone who's doing nothing but relaxing, and your moral system goes up because they were "evil". If your actions have to observed and plausibly spread information, then it's a reputation, but if it's instantaneous and doesn't have to be observed, it's likely "divine" (or similar like The Force in Star Wars).
There's also a point of what the goal is with the reputation system. Is it to push players to do good and/or punish them for doing evil? Is it to do the
reverse (there's a quote I hear a lot "No good deed goes unpunished")? Is it to explore the ramifications of both? Is it to sway the story and/or endings? Is it to lock/unlock areas, characters, etc? Is it to explore the meaning of heroism and villainy? The answers to these questions can leads you to different ideas.
Some tangible thoughts;
I've always loved the idea of the "underworld" where criminals come together in a sort of "merchant's fair". There's a specific one that comes up in roleplaying a lot where the players will only ever find it if they show they are the kind of cutthroat the underworld likes. If I were to put it into a game, I could see good reputation lowering prices in shops but bad reputation letting you go to (overpriced) stolen goods shops, making it a matter of "good prices vs more options".
For random encounters, a good reputation could have soldiers/guards/etc show up mid battle and give help (even just as single actions) while a bad reputation would add said guards to the possible enemy tables.
If the MC has damage and healing, better reputation makes healing better but damage worse and worse reputation vice versa.
"Random" loot could be determined by reputation, and it's especially a choice if weapons comes from bad reputation.