Hi Alex,
Great question! I'm changing a black interior in my '69 over to white. Some pieces are good & I can dye them, others are trashed & need replacement.
Just in case you missed it, here's a thread I did on headrests that were dyed from black to white. Going from black to tan should be even easier.
http://www.dodgecharger.com/forum/index.php/topic,45307.0.htmlAs long as you get a quality dye, such as PPG, DuPont, or SEM, you should have no problems. Most of the time, the mixed dyes like PPG & DuPont can be mixed in different gloss levels depending on the parts you're dyeing. That will lessen the "crappy" effect. The parts MUST be cleaned thoroughly, & use the proper vinyl or plastic prep sprays from SEM prior to applying the dye.
The dye doesn't really "penetrate" vinyl, it's more like a paint that adheres to the surface. As long as it's prepared properly you shouldn't have a problem. You don't want to load it on, either. Nice, several thin coats. The interior in my '68 went from green to black, & there are parts in there such as upper door panels that have been dyed since the late '80's that still look good.
Parts that are not heavy wear items such as seat covers should just be bought new in tan & not dyed. Other parts like the upper door panels, kick panels, seat hinge covers, sunvisors, etc can all be easily dyed.
Good Luck!