My mastiff mix used to be really reactive at the vet, but we've been able to work with him to the point that we haven't had a single incident in about a year (by incident I mean crazy barking, snapping, jumping at the vet, etc). He had a traumatic initial experience with one of the vets at the practice we go to, and he became dangerously reactive after that. The key with him was finding a specific veterinarian that he feels comfortable with (one that won't traumatize him), having him wear a muzzle, and coming up with a routine that helped him feel safe while he was there.

I know someone else mentioned that they prefer to not have owners in the room during appointments with reactive dogs because they will be upset by their dog being restrained, which is probably true in a lot of cases. Our solution was maybe a bit unusual/unorthodox (probably frowned upon by some people, but it works great for us). During appointments, I'm the one who holds him. I have him step on the table, the vet lifts it, I stand alongside my pup, and gently wrap one arm around his chest + one around his back (no squeezing!). He usually leans into me and settles in my arms, and when he's in this position he is able to tolerate the vet giving shots, doing a gentle physical exam, drawing blood, etc. My pup seems to understand that as long as I'm there holding him, nothing bad will happen to him.

I would like to address the fact that it is uncommon for a dog to enjoy being held like that, and that forcing a dog who does not like being held/hugged into that position could result in them hurting you. I just felt like it was worth sharing that anecdote in case anyone else has a fearful dog who loves being hugged/held. My guy is kind of big and scary looking, but deep down he is legit a big baby.

Other recommendations I have for making him feel safe/comfortable at the vet are pretty similar to what everyone else is saying. Giving him a positive association with the vet could go a long way. Also, if they aren't familiar with your dog, you definitely need to let them know about his reactivity before you bring him there. With advance notice, they will likely be able to accommodate him in some ways (making sure no other dogs are in the waiting area when he is brought through, having a muzzle ready if you don't have your own, having special treats out (my vet uses pureed chicken baby food on a tongue depressor), etc.