Depends on the store and what dog I have in the truck with me. The Basset & Treeing Walker ~ nope, in the truck they stay unless its PetsMart. If it is too hot to stay in the truck they stay home. The Aussie on the other hand - by my side. She LOVES TSC, the local Feed Store, ACE hardware, HomeDepot.
The guys at the feed store keep trying to convince me to let the Hounds out of the truck with her (since everyone’s dogs usually hang out in the loading bay) ~ but those two are notorious for getting on a scent and following their noses oblivious to being recalled unless on leash. And the Basset on leash is not the friendliest dog to everyone (someone forgot to tell him that adult males are not always going to bother me or my truck) - I get him out at PetsMart or the dog park for socialization off the farm, but even then I have to keep an eye on him.
My biggest pet peeve is people who just assume that a dog in the bed of a truck is there for them to pet as they walk by sigh
I would love to figure out how to mount a sign on my truckbed that says “Do NOT Pet the Bassett Hound” - if he is in the truck and a guy tries to reach towards the truck bed he will threaten to snap (so far he has never actually bitten, but it only takes once)…kids & women, no problems. The Walker - that overgrown pup will wash your face. The Aussie, well, if you have a ball she’ll get into YOUR car if we aren’t around to tell her not to (she’s been taken twice grrr which is another reason she goes WITH me when she is in the truck, or she is put into the cab)