Do you also look down on ur grandparent who also came from China?
Most of our great grandparents came from Qing Dynasty or ROC, not PRC. Peranakan families migrated here even earlier during Ming Dynasty. There're marked differences with post-cultural revolution PRC in behaviour, attitude, accent etc. It's not a matter of look-down, it's simply the difference.
Singapore all along has many PRs before the PRC influx. They were of course mostly Malaysian Chinese. There were not many complaints or conflicts about them all along. We have so many things in common and so used to each that it's hard to tell them apart from Singaporeans.
There's also a distinctive accent in Malaysian Mandarin, but that's considered pleasant. The PRC accent is usually considered irritating and obnoxious to Singapore ears. This PRC accent can lay no claim to Mandarin as it's supposed to be just because it comes from PRC. It's different from the dictionary-perfect diction of PRC and ROC TV newsreaders and actors.