There is also the "little" fact that his Dutch is absolutely terrible, as is Mathilde's...
As far as I know, they are both fluent, but they have a very thick French accent and that is what Dutch-speaking Belgians dislike. Apparently Mathilde is not a good speaker, she has a high voice and poor diction, so it isn't simply about language. I wonder if she had a speech impediment as a child, it might have influenced her career choices before her marriage, didn't she have her own speech therapy practice when she was single? Their children attend a bilingual school, in fact all the children of the royal family are being brought up to be fully bilingual, as they should be. I hope children in the Flemish regions get to learn French too.
In my opinion the issue of language has become politicized and it isn't simply about national identity. If Mathilde and Philip spoke flawless Dutch, something else would be criticized, maybe they would be called fake and calculating, because the criticism comes mainly from separatist groups and media, whose aim is to further their cause and they use that as a means to their end. It's not a little issue obviously, because they get slammed for it all the time, but personally, and speaking frankly, I find the idea that language is the sole identifying characteristic of a people to be small-minded and totally out of tune in the global age. You are what you are, regardless of what language you speak, and I say that as an American who was born in a Hispanic country, learned French as a child and English as a teenager.