Light and Radio waves are essentially the same, just at different power levels. Why can light not penetrate the wormhole?
Radio waves and visible light are essentially the same, except for their wavelength. The longer wavelength of radio waves allows them to pass through things that disrupt or block the shorter wavelengths of visible light. For example, you can still get cell phone reception in a building with no windows. For related information, see the Wikipedia articles on Faraday cages and EM shields.
The minor variations in the event horizon of the Stargate's wormhole must be a suitable size to interact with visible light. Otherwise, we wouldn't see the 'ripples of water' effect when looking at a Stargate. As the event horizon's in the way, we can't see past it to the wormhole and the planet on the other side of it. In fact, it would be interesting to find out what other species who see different spectra of light observe when looking into a connected Stargate. Anyway, radio waves are not effected by the event horizon's variations, and they're able to traverse the wormhole without issue, so the Stargate doesn't interfere with them passing through.