Is it permissible to contract with Google and place Google AdSense advertisements on an Islamic blog—taking into account that it is free of images or inappropriate advertisements—and is earning in this manner considered lawful, or is it a form of trading with religion?

If the blog owner can control the advertisements displayed, ensuring they are free from Sharia prohibitions and promotions of haram or objectionable content, then there is no harm in it, even if the blog is Islamic. However, if they cannot control them, and the advertisements will include prohibited matters such as usurious banks, alcoholic beverages, or immodest images, then it is not permissible.