The reason why it appears to "clash" is because red and yellow are in the same neighborhood of the spectrum. It's why you don't wear yellow and orange together, for example, without making the hues look very different from each other. Green and blue clashes more than green and purple. The individual colors on this site are not themselves "bright". It's just that they're near each other, spectrum-wise.
Personally, though, it doesn't bother me at all.