Would someone really have a low SOC in the Imperium?
Short answer: YES.
Fun fact ... LBB S4, p6 ... one of the mustering out benefits you can get as a Pirate is -1 Social.
I'm not sure how that would work.
In a word ... UNDERCLASS.
You're not a SLAVE (per se), but you're functionally a peasant or a serf or an indentured servant (the lower rungs of society).
"Polite society" (and everyone who wants to be in it) basically SHUNS you or treats you as sub-human, not deserving (or worthy) of respect, courtesy or even just simple decency and kindness.
If you want a historical parallel, think Victorian England and the "unwashed lower classes" ... or if you prefer a historical example more in keeping with the Hindu caste system, you're one of the Untouchables.
Other obvious options are being presumed to be a criminal, even if you're not.
Not exactly "racial profiling" but very definitely SOCIAL profiling.
How do Referees handle this?
Depends on how much "social interaction" goes on in a campaign.
A campaign populated with the stereotypical "murder hobos" isn't going to have a lot of socializing going on, so you can kind of get away with letting social standing be your dump stat.
However, the flipside to that is the stereotypical "only the cool people can enter the club" type situations, where people with high(er) social standing are allowed into places and can meet Important Patrons™ while people with low(er) social standing are denied access and lack connections to the upper social classes.
You can even have "snubbing" go both ways.
High social standing people are "not welcome" in low social standing locations, establishments and neighborhoods. I'm reminded of James Bond in Live and Let Die ... where Bond is tailing a car that is driving into Harlem, NYC. Doesn't go well for Bond since he's a white face (who speaks in a posh british accent!) heading into a black neighborhood and EVERYONE is watching him and reporting his movements, feeding the food chain of informants, keeping tabs on the OUTSIDER.