Absolutely!
We show the ovens in our videos and directions being built with Red and Tan firebrick as they are a great color combo. But as you said, some colors are not available in all areas.
You can build your oven in all Red or all Tan - the color of the firebrick has ZERO effect on the performance of the oven. There are hundreds of BrickWood Ovens across the country that are all red ovens and even more that are all tan ovens.