Depending on the company you work for and the whims of your immediate supervisor would you be allowed to bring your pet into your workplace?

The company I work for actually encourages us to bring our dogs to work, I bring mine two to three times a week. 

No.  I don't work now, but when I did it was at a grocery store.  Service dogs were allowed, but even then there was complaining. 

That wouldn't happen here.  I had a doctor for a short time who I really liked.  I met him while in the hospital and the first time I saw him at his office there was a St. Bernard in there.  I never went back.  I know hospitals and nursing homes have dogs brought in to help the patients' moods but a doctor office is off limits as it should be.  I was in a management position at the corporation from which I retired.  Neither the company nor I would have ever let employees bring animals to work.  It would be stupid to even ask.  Later, after I retired and when I worked on my own,  no one would have ever asked if they could bring in a pet.  I'm sure of it.  People have lost perspective.  Your pet is yours for you to enjoy. You.  In your own home.

I like the idea of pets in the workplace, however it might not work in all types of business. 

Given that I'm WFH right now, I could bring her in if I could trust her to behave, which I can't. The house is kid-proof, but not enthusiastic-Staffy-who-jumps-all-over-the-place-proof. She's the most affectionate pet I've ever owned, but Staffordshire terriers aren't known for being particularly intelligent and Skyla is dumb for a Staffy. We got her as a rescue, too old to train properly.

Comma after supervisor, eh. Pets in the workplace are not a good idea. Consider that customers and co-workers might be allergic, so it wouldn't be fair to them.

I am my own boss. I regularly bring my puppy to work. It is that or leave him in the kennel cage all day, and I did not want to do that unless no other choice. 
He is old enough  and trained enough that he does stay home now. Because it is cold and he hates my salamander heater. 

I've done it on occasion, in certain scenarios. I wouldn't do it unless she was specifically invited, or I'd gotten advanced permission. 

All of my jobs were in law offices and I've never worked in one that allowed pets.  Even if they were permitted, there may be co-workers who are allergic to them, so best not to start doing something like that.

The Navy wouldn't allow pets on the ships, but we did have a gecko stowaway in our shop. It was there until we got back to the states. In one of my classrooms I had small pets like rodents, snakes and a fish tank. I built a terrarium for turtles and frogs.