By and large, our local born Chinese respects our local Muslim community but with the influx of Chinese from Malaysia and China, these new citizens are more insensitive, eg. in tray return.
I witnessed muslim lady enquired about a cashier job at a Teppanyaki stall at Nex Foodcourt. The Malaysian chef pointed his finger and rotated around his face circumference, to hint to the applicant that she could not put on Hijab. In the end, the local supervisor (not the chef) still hired the lady.
This is a demeaning gesture that Malaysian Chinese used to humiliate Muslim women. If you are raised in Singapore, you wun do such things.