Unless you’re on public property (like a public school or government building) where carrying is prohibited by law, I think the most that can be done is ask you to leave. Now if you refuse the request it then becomes trespassing.
“No guns” signs in private businesses carry the same weight as “No shirt, no shoes no service” ones.
But the comment above that it’s best to just avoid businesses that prohibit carrying is the best option. Particularly if there’s a way to let them know they aren’t getting your business/money because of it.
Carrying on school property I believe is legal in Oregon. ..except if stupid student body bans it like they did at comm college in Roseburg