The e-m fields created by power lines don't affect the passage of e-m waves through the region around the power lines. [Technically a 'principle of superposition' operates, one of whose consequences is that beyond the region of the power lines, you couldn't tell that the e-m waves had passed through that region.] The interference you ask about is what you find when using a radio etc in the region of the power lines. The radio detects the fields due to the power lines and due to the e-m waves. What you hear may therefore not be what you want!
Why we say that light is not affected is because your eye does not respond to the frequencies of the fields from the power line. Your radio set does. Neither light nor radio wave themselves are affected in the way they travel by the fields from the power lines.