Hi Jehalepeno,
I would say it depends. Are the Islamic web designers only offering Islamic web services? If so, then no, they wouldn’t have to make a Christian site. That’s just like asking an Islamic meat shop to sell pork. If they don’t offer pork to begin with then you can’t compel them to sell pork products.
If they are simply web designers that are Islamic, and if they are offering a general service to the public, then that could get a bit fishy.
The gay web designer could refuse serving Westboro Baptist Church based on their hateful rhetoric. He is not discrimating against the baptist church at large; he is refusing this congregation specifically based on their hateful message.
Even if it wasn’t the Church but simply a member who wanted something innocent like a birthday design, the designer might choose to do business with the individual but if he chose not to serve that person based on their association with westboro, he would still legally be in the right. That may or may not be the right thing to do but legally it’s fine.