I'm very confused as to what the use of "rep" is for each side job. Does it just make those jobs more busy or increase earnings? For example after unlocking the gloryhole I rarely do the bar minigame, but it tells me my rep will decline. Is that bad?
Each rep does different things, but yes, they all make the job more busy.
As Neriel said, Bar rep increases "Bar Income" (10 first rep give 4% increase each, so at 10 rep, +40% bar income, 1% after that).
Gloryhole rep increases Staff Efficiency, which sounds good, and is good, but it's very hard to quantify and track.
If Strip Club rep is high enough, no floor will riot on a day when you perform at the strip club. Not sure what the exact rep limits are, but the max is probably around 30.
Receptionist job actually has 3 reps.
"Regular" rep simply increases the number of visitors, but the amount of order restored by doing the receptionist job depends on how many visitors you successfully processed, so more visitors means more potential gain.
Fame increases the number of visiting fans who just want to shake Karryn's hand. You can get a tip (and decent money) from them if you use the correct title, that makes them give you tips for handshakes.
Notoriety increases the number of lewd visitors, who ask Karryn to do lewd stuff.
Each job has some nice title you can gain at 30 rep. Receptionist also has a title for 30/30/30 rep (rep, fame, notoriety) IIRC.
