Do the different colours of sapphire affect the taste?
I'll go out on a limb and say yes, but with the preface that I consider myself quite sensitive, and unless sampled side by side, I doubt others would notice much of a difference. But I have red, white, and blue inserts so I can comment on them a bit.
I feel the blue sapphire edges the others out slightly, I can see the difference in nucleate boiling. I believe this is mostly due to thermal emissivity, as in, darker colors are better at emitting radiant heat. The same reason why a black t shirt feels hotter than a white shirt in direct sunlight.
As far as color affecting taste - colorant in synthetic gemstone is achieved with trace amounts of minerals, typically less than 1% of the composition by weight.
I have to note that I find the experience between a gem insert and terp pearls to be totally different. I pretty much never use pearls when dabbing, maybe if I'm going straight off Quartz, but I rarely pair with my sapphire inserts. I'd like to say the pearls help give an idea of how an insert will perform, but truthfully there's a big improvement with the insert IMHO.