I understand where OP is coming from. It's not about censorship, but rather a matter of good/poor taste. I love my local radio station, but every time they play Blurred Lines, I turn over and feel slightly disappointed in them that little bit more - a personal feeling of "Oh, come on, I thought you were better than that". The lines are not blurred, and I don't want my daughter thinking there's such a thing. Consent is consent - be clear and be heard.
Lost Prophets were never "banned" (there's no such thing now), but every media outlet knows that if they played their songs they would lose followers in their droves. It's a business judgement they make based on a moral perception. The rest of us probably don't listen to their music any longer in private as it reminds us of something so heinous. Michael Jackson is still played because he was never convicted, therefore he still has masses of fans who are quite happy to continue loving his work. Radio stations and TV companies are not arbiters of moral decency - they're corporations providing entertainment to the masses, and make judgements based on popularity. Netflix didn't pull House of Cards because they were disgusted by Kevin Spacey - their subscription take-up dropped massively because of how we feel about Kevin Spacey, so they decided to cut their losses (literally). It cost them millions to drop him (an un-aired movie, as well as the revenue HoC brought in), but they'd have lost more if they hadn't made this decision - it was damage control. I don't mean to ramble, but I think it's an important point to note that media are only as good as the standard we hold them to - and that "standard" is a very personal thing. When enough people's standards happen to coincide, then the media will follow.
When it comes to songs like Jealous Guy, I think it comes down to personal taste. Yes the song is probably about John Lennon's own experiences around domestic violence, but it's not immediately obvious to the listener - there's still room for interpretation. I completely get why it makes you feel uncomfortable, however.
Are the radio station right to pay it? Yes.
Are you right to switch it off? Absolutely.