Firstly I feel that you cannot really control and moderate what people are going to say at a funeralor post through your letterbox nearly as easily as you can moderate a face book page or your emails.
You can just throw leaflets in the bin, you can just ignore phone calls, you can ignore the person shouting at the funeral. At the end of the day what he was doing was harrasment, just because it is via the internet why should you have to put up with harrasment?
Secondly I am questioning at what point does being insensitive actually come a crime? Why are tasteless jokes after even such as the Japanese tsunami perfectly socially acceptable but something like this is so horrible? Thousands of innocent people die, that's okay to lul about, but a blonde white girl tops herself and making lulz are completely out of the question. How does that work?
Context would be a start. i.e. making jokes on a forum where it is unlikely the family involved would see it is completely different from deliberately targeting the family. Much like making tasteless jokes about the tsunami is fine in some places, whilst doing it at a memorial for them would be out of line.
No, I don't think it should be a crime to call a person an abuse them about their dead daughter. It's a rather distasteful thing to do, but the law should not extend to such trivial things. If I were on the receiving end, I would put the phone down, and if it became a course of action, block the phone number in question.
I would also have no problem with a person printing leaflets and dropping them round friends' and relatives' houses.
A slightly more consistent approach than the poster quoted above and I can sort of see what you are saying, but I am not exactly sure that harrasment is such a trivial thing as you make out. The fact that you are able to easily deal with it does not automatically equate that everyone can easily deal with it. At the end of the day this guy was deliberately setting out to annoy, upset and harras people. Just because his chosen medium was the internet does not mean he should not face censure because of it.