It's quite offensive. English is my native tongue, I got a perfect IELTS score, and one of my parents was an English professor. But my accent makes me less than "native".
It's often required for immigration purposes. Countries/Universities will let you off where you're coming from a country that has english as it's main language or have studied a degree in the language, but they often won't if you're a native English speaker living elsewhere.
The first two days were a shock, as I felt it was a different language. But just after some time, god adjusted. And I find endearing both Singlish pronunciation and phrases.
For example, the first time I hear "ondah-cah?" I was puzzled. Then understood that it is "Monday can?". Which, as I learned, means "Would Monday work for you?".
