Why do a lot of "moderate" Muslims seem to focus on pointing out atrocities committed in other cultures instead of directly addressing practices that are prevalent in a lot of Muslim cultures?
Stoning is not merely a cultural phenomenon that arose or continued to be practiced out of the blue without any relation to Islam;
many Muslims believe that stoning is an Islamic punishment. The two main hadith books (which are considered authentic by the majority of Islamic scholars),
Sahih Bukhari and
Sahih Muslim, also contain hadiths that explicitly prescribe stoning and
ones that directly attribute instances of ordering the punishment to Muhammad.
If you ignore the hadiths that are considered authentic by most Islamic scholars and say that stoning is not Islamic, that certainly doesn't mean the religion doesn't contain ammo for those who see such punishment as a divine mandate. There
is support for stoning in more than one place in Islamic texts (like the hadith books I mentioned above), and claiming otherwise indicates either lack of knowledge of what the majority of Islamic scholars state or lack of knowledge of Islamic texts themselves.