Because those shipyards wouldn't neccessarily stop producing ships for their own race just because they're members of the Federation... and likely, the new ships being produced by those racially owned shipyards would probably be appropriated and refit for starfleet use during times of war.
if someone else wants to play in a vulcan ship, (as you can guess from my avatar, im one of them) why is it any skin of your nose. just pretend its some random science ship flying past you with a vulcan crew aboard.
or that starfleet have decided to include new ship designs. not every new ship has to have a saucer and two warp nacelles. starfleet ships have been based off earth designs for 300 odd years, there is no reason they cant build starfleet ships based off vulcan or andorian designs.
It's clear all the way back to the Task Force Hippocrates mission in the game that the Vulcans have a capable space fleet independent of Starfleet. Also as an FYI, the D'Kyre class replaces the Vulcan ship in that mission. The dev's posted a screenshot of it here.