Im not sure you can say the Mosque IS built by radicals Kemp, one sentence from one man does not make the group radicals.
I personally understand your view point about it being too close and the backlash could affect moderate Muslims in America however I am going to play devils advocate for a second.
To me it shows that America is not a bigoted judgemental country, it can discern between the minority terrorists who claim to be Muslim and the actual Muslims practicing the faith. It sends a clear message that the country is not anti Islamic but anti terror.
It is almost an extension of the "non negotiation with terrorists" policy. Al Quieda are not capable of dictating American policy - they tried to cause a division between Christian and Islamic Americans and look, working in harmony to spread understanding near the 11/9 site.
It also provides a victory for the moderates over the radicals, they are not being treated the same by the Obama administration, the distinction is clearly there - the evil Imams that exist to convert people to radicalism can hardly say look at how America treats us when this Mosque is built.
Nor is it disrespectful to the victims, the Muslims building and praying in the Mosque did not support nor take part in the terror attack, they had no links and will not be glorifying it, the fact they are Muslim does not matter, it would be like war veterens protesting outside Sony America saying that having a Japanese business in America is disgraceful and disrespects the war dead.
Finally, there are many Americans who simply do not understand Islam, ignorance can lead to fear and mistrust, this is an education centre that will encourage non Muslims to visit and speak to the members about Islam - you cannot win the current war on terror through conflict - Afghanistan has proven that (the fact there is negotiation with the taliban now to bring them into the Afghan government), education might help go a step further in ending the terror threat at home for a start.