Having been a school owner before, I see nothing racist in saying that I only want native speakers to apply. First of all, this has nothing to do with being black, yellow or white. Native speaker does not mean handsome white man or woman. It simply means some one whose first language is English, and if it's English conversation that you're learning, then there's nothing strange about wanting to learn it from a native speaker.
Secondly, and anyone who has ever posted a job ad on ajarn would know this, even though you may state you are only looking for a native speaker, you will get at least 300 resumes from Filipinos. Also, the fact that they are Filipino will be hidden. So you will actually have to read through the entire resume to finally find out that they are Filipino, and that you have wasted your time reading their resume. It's very frustrating.
Let's say for instance I wanted to open a Tagalog school. I would put out an advertisement for Native Speakers of Tagalog, and not those who are from America and learned it at school and speak it really well. This is not being racist, it's not being prejudice, I just want some one whose first language is Tagalog. And if every time I advertised I received thousands of resumes from Americans who hid the fact that they were American inside a very small part of their resumes, I would want to make sure that the Americans understood that I do not want them to send me resumes.