Eugene Volokh has an article giving a good run down on Constitutional limits on picketing. Here’s the short of it:
It turns out that the government (a) can ban loud picketing outside funerals, and (b) can probably ban all picketing immediately outside the funeral, but (c) must allow picketing or marching relatively near to funerals. How near is impossible to tell, but picketers can’t be required to stay 300 feet or more away; they probably have to be allowed to march past the funeral, and perhaps even to picket, say, 100 or 200 feet away.
I’m not sure if the statute the ACLU and Westboro Baptist Church are challenging would survive Consitutional scrutiny as I have not read it. It’s probably a safe bet that if the law is content-neutral (I’m assuming it is unless the legislature likes to enact laws that are obviously going to be struck down), then it will survive. Anyway, we’ll have have to wait and see.