Gensōiri (幻想入り, lit. “Entering Gensōkyō”) refers to the act of entering the elusive land of Gensōkyō from Touhou Project. It used to be a fairly popular subject in the past, which eventually inspired enough fan works and crossovers that it sorta became its own isekai subgenre.

The land of Gensōkyō and the outside world is formally separated by a barrier that Yukari Yakumo had set up, called the 'Boundary of Illusion and Reality' (幻と実体の境界), which generally allows weak youkai to enter.¹⁾ Since the human imagination is still capable of creating new youkai, these youkai can technically enter, but will typically vanish as they lack details, form, or lack the staying power that traditional youkai have.²⁾

In addition, you have the 'Great Hakurei Barrier' (博麗大結界) that can technically be weakened enough to let any 'outsider' (外来人) or lost item pass through. However, most outsiders have an incredibly low chance of survival, then their belongings wind up in Muenzuka to be collected. If they do survive, they can be returned to the outside world or, in very rare cases, voluntarily settle at the Human Village.³⁾

Other factors include the whimsical and unpredictable nature of Yukari Yakumo, as she has the ability to drag anything into and out of Gensōkyō at will, an especially popular reasoning among fan works. As the series develops, we also have cases like Kanako Yasaka who sorta 'entered willingly', and Sumireko Usami who has that whole 'dream soul' (夢魂) situation which allows her to have a 'dream self' in Gensōkyō.

The term may also refer to the abundance of fan works, including crossover works, typically placed under the Gensōiri Series (幻想入りシリーズ) tag. One of the earliest fan works is “Ore ga Gensōiri” (俺が幻想入り), uploaded to Niconico on October 6, 2007,⁴⁾ that was authored by “Pentagon” (ペンタゴン) and had the luxury of audience participation with questionnaires on how to progress the story.⁵⁾

Much of the appeal behind a Gensōiri work, compared to regular fan works, is that they can be an interesting starting point if you wish to bring in a new outsider's perspective or bring about a domino effect as these additions could easily trigger a new development or incident. However, the genre sorta shifted to the latter over time since you can only write a testimonial in so many ways, especially after Sumireko Usami.

On the other hand, these fan works generally face the same 'criticisms' that fan works normally get when you add in a new character: Does the new character come off as a self-insert (e.g. Mary Sue)? Does the characters or the settings feel 'too derivative' from the source? Does their relationship or power dynamic make sense? Would the interactions feel too skewed from the audience's perspective?

• The inverse situation is actually called 'Gendaiiri' (現代入り, lit. “entering modernity”).

• Gensōiri + Gensōiri Series on Pixiv Encyclopedia
• Gensōiri + Gensōiri Series on Niconico Encyclopedia
• Gensōiri AtWiki