What is the ruling on placing an advertisement for a news or Islamic website in my forum, knowing that it displays Google AdSense ads, and what prevents placing Google AdSense ads with the possibility of filtering them and preventing the appearance of images of women or alcoholic beverages?

It is permissible to include advertisements in the forum provided they are free from Sharia prohibitions. If you are unable to filter them, then it is not permissible to place them. As for placing an advertisement for a news or Islamic website that displays mixed advertisements: if the website filters its advertisements to avoid what is unlawful, then there is no issue. But if it does not filter them, then advertising it is questionable. However, it is not ruled as prohibited because the website itself is permissible, and the advertisements are subordinate to it.