Vulcans are arrogant, not racist. I'm sure serving on a ship full of ONLY Vulcans would just make things worse.
Frankly, I want to know who allowed a Starfleet ship to have an all-Vulcan crew. What possible purpose could that serve?
Probably the same purpose as a ship with an all human crew, or an all Andorian crew (I don't remember of that ever came up). To make the crew more comfortable by being surrounded by their own kind? That's admittedly a very loose guess, but it would make sense.
Another possibility would be sending a ship crewed a specific race is because certain races cannot handle certain sectors of space for whatever reason, similar to the way the Expanse had a negative effect on Vulcans in ENTERPRISE.