Let's not make it about race? When the agent lists the property as "No Indians, No PRC" I don't think you can quite get away from making it about race.
"No Indians, No PRC" can also mean bias on citizenship (i.e. politics)! That might be especially so when the same (Han ethnic) Chinese from HK or ROC would meet no hardship. So it may not necessarily be the race (or at least not for all landlords) as it may be the way they expect that their tenants will think or behave. It's called Memetics, and until naturalization in a new medium the individuals may present a higher risk of getting themselves at odds with the others around them.
Except no one asked "Is she Singaporean born, ethnically Indian?"
Just saying her name was enough to get rejected.
Actually, they might be referring to nationality rather than race. For example, it very common for landlords or their agents to ask about your nationality. They might be fine with a Singaporean Chinese, but PRC, maybe not.