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".
Singapore is a “native” English speaking country yet has an extremely distinctive accent.
(usually seen as a negative by both Singaporeans and non-Singaporeans)
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?".
I would have done it regardless, because it got me extra points.