For Bella it depends on the situation.
If we have her out in public, say the diamond for instance, she is very watchful and aware of everything that is going on. If I leave to throw a poop bag away, her eyes are on me at all times and she walks alongside the fence to "follow" me to the trashcan and then back and she will wait at the gate for me to come in. If someone is walking by, she watches their every move until they leave and sometime, she will go to that area and walk them along (to us, this is very cute, lol).
If we take her to pet store, she has a vest that says do not pet that we put on her. She often has let people pet her, but she calls these shots and I would never make her approach someone because they want to pet "that cuuuute doggy!" If someone asks if they can pet her, I explain to them that only if she will let them. For those that don't know the breed, we usually get a shocked, what the hell, look; for those that may be familiar, we usually get a bummed, I understand, here's hoping she comes to me look.
If someone comes into the home, it's completely different. It's her territory. And she lets every single person know that. When we know someone is going to come stay with us, we plan on having Bella meet them on neutral territory. When my mom came to visit, her train ended up being several hours late and it was near midnight. So Bella met her here at home. Bella was never okay with my mom being here- I feel it's because she didn't like her (my mom paid no attention to the fact that she would need to visit often if she wanted to be fully accepted by Bella- my mom didn't come until she 9 months old and by that time, her idea of "family" was already in her mind) and that we didn't do the appropriate on meet on neutral territory thing.
When my best friend came to visit, thankfully, they were able to meet on neutral territory and it went well. By the time my friend left, she was getting fila kisses and was able to be semi-alone with Bella.
Vets are a whole different story. I was so p.o.'d when our vet unexpectedly retired because he had been working with Bella from day one. She was comfortable with him. Still grates on my nerves a bit.. Bella never liked the vet that saw Buddy, so we found a new one. Their first meeting when great, we "presented" Bella to him and he was very aware of her breed and how she would be-thankfully.
The eye doc is yet another different story. We've not seen one doc every time. We've seen a total of three different ones, for check ups, etc.. and one we had only seen once actually performed her surgery. Thankfully, almost every time the same tech has been there and she has slowly been gaining Bella's trust. When I dropped Bella off for her surgery, she had to be pre-sedated, so she was pretty out of it. But a different tech tried to approach her and it didn't go well. Now, they know how serious we are when we say she needs consistency. The last time we went for a check-up, Bella jumped up on the bench with me and let Andre- the tech, sit with us and pet her. No one else is able to do that. Again, it's all on Bella's terms.
I think most of it depends on the owners, as well. If we're okay with something, then Bella is okay with it, too, but at her own level. Walking through the pet store, Bella is not going to rush to every stranger to be petted and even though I may think it's okay for so and so to pet her, it doesn't mean that she thinks it's okay for so and so to pet her.
In the few times we've had complete strangers over (to fix something, etc) she has growled. She's never bitten, nor attacked anyone. I think someone would be rather foolish to try to harm anyone in this house with her around. Her growl alone would stop anyone with a half a brain in their tracks. With that said, there has been one instance in which Bella has lunged at an individual. In this instance, her actions were completely warranted and she has proved to be an excellent specimen of her breed.