I've camped in odd places in the past. If I didn't like where I was, I'd just bring the bike into the tent with me. No trailer.

I take my bike out shopping quite a bit. I always lock the bike, but it is impossible to secure everything in the trailer. If I have $200+ worth of stuff in the trailer, or something that seems particularly tempting, I sometimes avoid stopping. But, so far, no problems.

The annoying thing is the stores that prohibit backpacks. No, not the big hiking packs, but the little purse-sized ones.