I'd have to agree with applepievn's summation to a large extent. When I bought my HDB flat 12 years ago, it was rather funny in the beginning as where I'm from we ALWAYS greet people in the neighbourhood when passing, even if it's only to say good morning/evening. In fact, once you make eye contact, a greeting is almost expected. So, when I was doing the renovations to my flat, I was back & forth to the hardware & electrical shops daily/several times a day. I pass someone, I'd greet them. I'd also get funny stares as they stammered and hesitated before returning a greeting.
I often said, in response to the lack of courtesy here, that it starts with you. If you don't confront discourteous head on, then you are tacitly agreeing with the inconsiderate behaviour. Will it make a difference? No. Not immediately anyway, but as more and more get the message that it's not okay, then change, albeit slowly, starts happening.
So, my neighbours in the estate (and not just the ones in my block) finally figured out that that crazy angmo is going to speak to me come hell or high water, eventually, even if I didn't they would greet me cause they knew it was coming. Now, in my estate, I see them greeting other's who are not necessarily Singaporean or of the same race. It's a good feeling. Whether they take it with them outside the estate is another story, but changes can be made. Even if it's by a crazy angmo who they, for some strange reason, always thought I looked familiar!
It is very hard to bridge the difference, the east/west divide, especially in the heartlands. It's easier today, but 20 years ago, it was virtually impossible without meeting them further than half way. I found, what for me, was an ideal solution, that worked better than I had ever anticipated it would/could. I'm basically an introvert. But I started working part time for SBC back in 1988 as a part time actor. In 18 years I acted (not as an extra) in over 100 Mandarin drama serials from 1988 to 2006. I've acted with all the old famous one including Zoe Tay (Pretty Faces) and Fann Wong (Golden Pillow) to just name a few.

This has made me easily recognized in kopitiams, buses & MRt trains. So, even the office kopi lady has seen me over and over again, including even today as they are all being run in the afternoon rerun time slots as well. So, even with very little English at all, the curiosity gets the best of 'em. "You, ah, SBC izzit?" So if I happen to know which series is on I'll reply "Yeah, Mr. Brown" or whoever. All the barriers come down immediately.
One just has to find out what works, and you can bridge the divide.