It depends on the dog. If we are at a pet supplies store and there is an older collie type dog on a leash that acts very calm, I don't pick Mia up. I actually let Mia become friends with two 10+ year old bigger dogs in the past. But, those guys were obviously docile, were spending significant energy just walking around, and Mia is on the bigger side (she's 10 lbs.). Plus, Mia is very submissive and friendly towards other dogs. If Mia was smaller and agressive towards other dogs I would not have taken the chance even with senior dogs.
On the other hand, if I see the neighbor's "intact" rottie, I cross the street or pick Mia up because even from afar it is very obvious that the rottie is looking to pick a fight. I don't think there is anything for big dog owners' to be offended about.
Sometimes baby Doxie or Chi owners that carry them around on lap, don't let their dogs on the floor to meet Mia, and I don't get offended at all even though Mia is a friendly toy dog as well. She is well-built, what can I say?
Whatever makes the owner comfortable is cool with me, because in the end, the dog is the owner's responsibility. Better safe than sorry.