“Google did not come up with the Muslim search site.”
They had Googles permission to do this:
According to the Web site, it uses the database of the well-known search engine Google and is powered by it, but filters search terms in accordance with Islam.
It is stated on the Web site’s “About Us” section that the engine was built on the substructure of Google and anyone could build a similar site. Some terms are not available to search at all, while in the results for searchable terms, results about Islam come first. “The best search for Islam,” the Web site states on its main page, on which the color green, known as Islam’s color is used.
...
http://www.hurriyet.com.tr/english/domestic/10771723.asp
Which means Christians, Jewish, Buddhist ... can do the same thing.
Would you have a problem with a Christian based website that used the Google engine but limited searches to sites acceptable to their beliefs?