Related Q: Do Americans discriminate against Australians with strong accent?

I would say minimal. Basic criteria — if you can 1) speak English enough to be understood and 2) write English enough to make your points, then Americans would accept your English.

In many big American cities, non-native speakers account for 15-30% of local population. Singaporeans are among the best non-native speakers.

Similarly, do mainlanders discriminate against Hongkong or Malaysian Chinese on their oral/written Chinese?

I would say the written form is rarely subject to ethnic discrimination.