Good point on the "funds to immediately replace it". To me that is a key thing. You have less need for worry if you choose bike and gear that you can afford to replace. It is quite possible to choose suitable equipment in a pretty low price range and if money is tight it makes sense to do so.

I have had a couple items go missing on tour, but always when I left them in plain sight, like a pump tucked under a strap, where the temptation to just grab it was too high. I have never had anyone open a pannier and go through my stuff.

Dirty clothes and used camping gear are not all that tempting to most thieves, but in some places bike theft is common. Bike friendly towns are the worst and bike thieves are common in some of them. Small towns are usually pretty safe. I wheel my bike down the store aisles with me if I think the risk is high and leave it out front if I think risk is low. Barring that bringing it into the store and parking it out of the way in the front of the store shouldn't be a problem other than in really small general stores where leaving it outside is usually pretty safe. I take a very light "honest people" cable lock and use or don't use it depending on where I am.

The other thing is that I spend very little time in or near cities when on tour.