How to I block advertisements for one specific app?
Since these objectionable ads show up in multiple apps, they are likely being mass-distributed by a large advertising provider company (such as Google).
I don't think you'll be able to successfully block ads for a single product that are distributed this way, but since the content of the ads is questionable, you can determine which ad provider is delivering questionable content, and file a report with them.  If the content being pushed is illegal in your jurisdiction, you can also involve law enforcement.
Finally, you can notify the developers of all the apps in which you see these ads and let them know about the issue.  They can then file a report with their ad providers and consider finding more suitable ad providers.  If you leave accurate reviews regarding this issue, you may be able to pressure the developers of the apps you use to find a more appropriate advertising provider or remove the advertising content altogether.  Often, you can purchase paid versions of apps that have no advertising.