Depends on the individual and species, however, I'd like to update you with some information I found specifically for human outsiders that I found.
The latest chapter of CoLA has this to say regarding them
Gensokyo's youkai are forbidden from attacking humans. Why? Because they know that if the humans die out, the youkai can't keep existing either. So they settle for 'scaring them practically to death', at worst. However, with regards to the humans who disappear into Gensokyo from the Outside World, the rules are left unclear. Some violent youkai say that unmanaged Outsider humans ought to be fair game. Conversely, other youkai argue that because the Outside World keeps its humans under even stricter management than Gensokyo, laying a hand on them could lead to Gensokyo's discovery, putting its very existence in peril.
I also recall (though I might be entirely wrong here and might not even be canon, so take this with a major grain of salt) reading that all three factions of the Animal Realm mafia are essentially interested in keeping outsiders alive, because they want them to be recruited for their cause (I don't recall where I read this however, it might be a misinterpretation of one of CoLA's chapters or one of the endings of the latest game that I read, or somewhere on the Touhou wiki), I could be entirely wrong here but seeing as animal realm entities tend to often appear on the surface and they are indeed looking for more beings to spice up their numbers, I wouldn't call this theory farfetched.
This plus Aya's article from SoPM stating that outsiders are so incredibly rare to spot that youkai literally need to change their diets and all leads me to believe that your odds of surviving in Gensokyo as an outsider is higher than you may think. You may want to spawn as closest as you can to either the Hakurei Shrine or Gensokyo (Kourindou is also okay though), bonus points if you have apparel that mimics the human villager's clothes, because even violent youkai may mistake you for a regular human villager and may decide not to attack you (at worst, they could toy with you in order for their boredom to be relieved), just
don't spawn inside Youkai Mountain (unless you were near the Moriya Temple, which is also fine)
Though even if you were not attacked or taken to be the lunch of a youkai, being a minion of the Animal Realm beasts isn't likely to be all that jazzy, so avoid that if you can. Because you'll likely be facing grunt work (aka, the boring chores) or you'll be used as a host for other animal realm spirits to be possessed, and is unlikely that they'll treat your body very well so yeah, keep that in mind.
Human Village what everyone else said, working under conditions of feudal Japan and knowledge of that era, not fun but you do get access to Akyuu's library and knowledge if you can chance a meeting with her (and a conversation with Keine might be the coolest thing if you're a history buff) so likely not all that terrible, you may even get to be given a small house somewhere or something. Which, given the prices of real estate globally, that may be a boon in by itself :P
Youkai and Gods what everyone else said. With the caveat that there's more limitations on youkai regarding outsiders so they may need to find new diets or even hobbies. Gods also what everyone else said, though it depends on what kind of god you are and what your specialty is you may need to put more effort than average on specific seasons (like Shizuha for instance).
One more thing, shinigami don't hunt hermits, they give warnings but is not their job to hunt for them. The ones who hunt for hermits are Kishin, and from what I've seen, primarily nasty cases of them (like Seiga in WaHH), Kishins are no joke though so you may need to train a lot in case you get spotted by one.
That's about it
