From my own experience, it really comes down to the school. At my school, there is not a problem having two or three non-native English teachers on the regular program, teaching English. They would prefer not to, but it is a question of $$$.
On the more prestigious English Program this is not an option and, as such, we have found it very difficult to find suitably qualified, native-speaker math and science teachers.
Two years ago, science was taught by a very-well qualified Filipino teacher, however, the students found her accent hard to understand. The following year, an agency supplied a much less qualified native speaker.
Despite the fact that he couldn't teach, he was still prefered as a) he was a European and b) he was a native speaker; albiet from Newcastle, but his command of bar-beer 'bamboo' English was astounding.

Personally, I have to agree with Hero, but the underlying prejudice against non-Caucasian teachers will always be lurking under the bright Thai smiles.
Incidentally, the best English speaking Thai teacher that I ever worked with had studied in India, and spoke with a bit of an Indian accent. That was never an issue though.