Without going into too much detail (because I am not well read on this and am likely to be wrong about a lot of it), one of the many issues that Abe addressed during his leadership was Japan's declining birthrate. There's a bit of a conspiracy amongst many people who consume Japanese popular culture (at a deep-ish level) that Abe pushed pronatalist themes in pop culture, as well as tropes like NEETs/hikikomori escaping their isolation from society and entering romantic relationships. This has become a huge meme, where any time a romantic development happens in a manga or anime, many people are quick to say things along the lines of "Abe would be proud".

E: From the knowyourmeme page on Abe:

Japan has seen a declining birthrate and population in recent years, which has been blamed on young people in Japan being uninterested in having sex. However, due to sexual content in many anime, including shows like Darling in the Franxx whose plots seem to encourage procreation, people have joked that Abe is using anime to encourage Japanese young people to have sex and start families. These are particularly popular on Tumblr. For example, Tumblr user justintaco posted a photoshopped image of Abe superimposed on a screenshot of Darling in the Franxx, gaining over 36,000 notes (shown below, left). User freyjaofthenorth made a similar post about the anime Conception, gaining over 2,900 notes (shown below, right). There is also a mock Tumblr for Shinzo Abe devoted to this joke.