Is reading advertisements that include forbidden things—whether free of women or with them present without looking at them—unlawful in Islamic law, and what is the evidence for this from the Qur’an and Sunnah?

The default rule for things is permissibility, except for what is prohibited by evidence. Reading advertisements that contain prohibited things does not deviate from this principle unless a forbidden consequence results from it. If it is known or thought that reading them will lead to being influenced by their content, or the spread of their news, or the promotion of their prohibited content, then it becomes forbidden; because the means to the forbidden is forbidden. If it is free from these prohibitions, it remains based on the principle of permissibility.