I don't know about tumblr, but reddit doesn't allow nsfw subs out of the box on mobile, and for logged in users, you have to explicitly enable it.

Obviously you can still find nsfw content on reddit that isn't labeled as such, so beyond that, it's probably up to the developer's soft skills. reddit probably has some people who are good at framing the app in communication with review, escalating review decisions, and communicating content policies in a way that makes them seem consistent and trustworthy.

I don't know about tumblr, but unfortunately, I don't think many indie apps with user-generated content would have the bandwidth to develop the same relationship with app stores. So there is some de facto gatekeeping happening that benefits the largest and most well-spoken social networks.