There are some people who play the Never Leave The Farm challenge and this type of interaction could satisfy a non-combat and possibly a non-supernatural playthrough. Expanding this to a Pelican Town-limited playthrough might be possible as you can avoid:
• the Wizard by never entering his Tower
• the Secret Woods altogether
• the Sewers by not entering them
• the Mines by not entering them
• the Community Center (after the initial cutscene)
You'll never get to Ginger Island but that's even more supernatural so should be avoided anyway. So what can't be avoided:
• Crop Fairy
• Witch flyover
• Strange Capsule (you could explain this as a prank as nothing comes of it)
• Initial Community Center cutscene (hey, Lewis sees nothing and neither can you if you want, it's just rats)
What are not
necessarily supernatural?
• Meteor
• Stone Owl (it just got uncovered, that's all)
• Bigfoot-thing (it's

Sam in a suit pranking you)
•

Emily's dream (it's just a dream, right?)
Pondering more I think you'd need to go the Joja route to enjoy the Desert by fixing the Bus but that makes me think, what Festivals would you need to skip?
• Egg Hunt is OK
• Desert Festival may be OK if you view the racers as remote control cars.
• Flower Dance is OK
• Luau is OK
• Trout Derby is OK
• Moonlight Jellies is OK
• Stardew Valley Fair seems fine as it's typical carnie sideshow stuff, just avoid Welwick which I do anyway
• Spirit's Eve could be OK but you may wish to skip, depends on your interpretations of things
• Festival of Ice is OK
• Squid Fest is OK
• Night Market can be OK, maybe skip the Mermaid Show (which I would never skip even if there was no free Pearl)
• Feast of the Winter Star is OK
Of course I'm sure I'm missing things but I'll add them if I remember.