It seems like the camera and lens shouldn't matter, but I've been wrong before. Can cameras like the Graflex Speed Graphic or Tachihara 4x5 field camera, and lenses like the Ektar 127mm shoot color film simply by swapping the type of negative in the film holder?
The camera doesn't matter.
The lens might.
Many older lenses used glass that contained chemical elements that can shift color over time. Most notable are the lenses that used glass containing radioactive thorium oxide that yellows and eventually browns as it ages.
Some of the most well known lenses containing thorium were several of the Kodak Ektar and Aero-Ektar lenses produced between the 1940s and 1960s.
If the color of the lens has shifted over time then there would be a color cast on images captured on color film using such a lens.
Even with B&W film the color cast of the lens can affect the relative tonal values of the various colors of light passing through the lens in much the same way that a color filter affects the relative tonal densities of differently colored objects on a B&W negative.