If a chaotic character has a reputation for being chaotic, wouldn't that more logically be a penalty to Bluff, since everyone knows they're chaotic?

I think social skills are too context-driven to say reputation for alignment X gives bonus to skill Y.

In d20 Modern, reputation was simply a check to see whether your reputation was known - literally, to see if you were famous or not. The exact kind of reputation would be based on RP and past actions, so the typical PC would eventually be famous for being a "murder-hobo".

The modifier for being famous was always +2 or -2, and it would depend on how that particular PC reacts to your kind of fame. Personally, I'd expand that, so that particularly strong reputations could grant bigger modifiers.

If I were going to base things on alignment at all, I'd give serious thought to having a reputation for being lawful grant a bonus on Bluff checks. Because, ya know, no one expects that. Plus a bonus on Intimidate checks against chaotic creatures, and Diplomacy with other lawful creatures.

A reputation for being good might grant bonuses to Diplomacy with good creatures only (and penalties with evil ones), plus penalties for Intimidate with everyone.

A reputation for evil might grant a bonus to Intimidate and a penalty to Diplomacy.

A reputation for being chaotic would grant a penalty on your Bluff checks (because people know to watch you), but a bonus on Intimidate against lawful creatures (because that much weirdness is unnerving for them). It could also grant a bonus on Perform checks because your unpredictable antics are more entertaining.

All reputations should grant penalties to Disguise checks when disguising yourself, and a bonus on Profession when used to generate incomes.