We had a similar experience. One of the vets in the practice we go to was hesitant about seeing our F5 SBT boy because she had never seen a Savannah before. Once she met D, she was in love, and now sees Mickey pretty regularly (mostly because she is in the office on Saturdays, and he LOVES to get into things on Friday nights).
That said, Jarvis, our F3 boy, is nervous at the vet, and as a result, I only book him (for well visits) to see the vet who handles the exotic cats, and he always goes with D along for moral support (D LOVES the vet and helps Jarvis feel less nervous). If the vet is hesitant, it can go badly for the vet and the cat IMHO.