This is a culture thing, nothing to do with being conservative/liberal. Renting in Singapore is expensive, therefore people prefer to stay with parents until they can afford to buy their own HDB.
Actually you are not allowed to buy HDB (apart from very special exceptions) if you are not married. So one joke goes how to propose (marriage): you, ... you want to apply for HDB?
Has everything to do with conservative/liberal. Living with parents your whole life until marriage produces conservative non risk takers, and there is a conservative political policy behind it that prevents you from obtaining HBD housing until you marry.
I think it's really just more of the ruthless pragmatism that makes this place so efficient and a consequence of land scarcity. Housing is limited and leaving it up to the free market would exacerbate wealth inequality. Therefore the government steps in with subsidized housing, which almost by definition will have more demand than supply. Prioritizing young families makes sense as the birth rate is below replacement.
This is a culture thing, nothing to do with being conservative/liberal. Renting in Singapore is expensive, therefore people prefer to stay with parents until they can afford to buy their own HDB.