MuraPichi

MuraPichi is the non-binary ship between Villager and Princess Peach.

Canon
The default male Villager has a similar color scheme to Mario, to wit, they both have brown hair and their clothing is dominantly red and blue. The default female Villager has a dominantly pink color scheme, much like Peach herself.

Peach in Animal Crossing
In New Leaf, when purchasing a fortune cookie from Timmy and Tommy's shop, it is possible to win Peach's parasol. The description states that she who hides herself from an angry sun does so with dignity, referencing the Angry Sun enemy from Super Mario Bros. 3. It works just like a regular parasol, though it is much, much smaller.

In New Horizons, the craftable "Tulip Surprise Box" item has a doll resembling Peach, Princess Daisy or Rosalina pop up by chance. A later update allows the Villager to dress up like Peach, which was previously only possible through custom designs.

Super Smash Bros.
The Twitter account for Nintendo of UK posted a picture of Villager and Peach on Valentine's Day, 2016. The caption quotes "Villager's top Valentine's tip", saying that when dancing with your crush, you should bring out your best moves. The picture shows Villager and Peach dancing next to each other.

In the Spirit fights for Daisy Mae and Joan, Peach fights alongside Villager. She uses primarily turnips as attacks, referencing that Daisy Mae and Joan are turnip sellers.

An official screenshot on Peach's page on smashbros.com shows her "gardening" with Villager. The male Villager seemingly unearthed a turnip with his shovel, showing it to her, Peach appears to be shocked.

Fanon
The ship is a rarepair in the fandom, though it does have its fans. People were enticed by the implication that Villager has a crush on Peach, adding fuel to the ship. Others came naturally, arguing that they have a lot in common, they're both rather calm and enjoy gardening. A good chunk of fanwork for the ship references turnips, having Peach give an excited Villager a turnip, which potentially means a lot of money for them. Darker takes on the ship have them holding turnips with suspicious red liquid dripping off of them.

The het and femslash variants seem to be roughly equally popular.

The pairing has two fanfictions on AO3.

Fandom
FAN FICTION