I don't know any artisan pipe makers staining the inside of a bowl. Most, including myself, are very careful when applying stain as to not get it in the pipe. Occasionally a drip occurs on the rim and I sand the bowl to remove the stain.
I've used an unflavored gelatin and charcoal mixture for a while now and do not notice a bad taste only a neutral taste while breaking a pipe in. On untreated bowls, I notice the briar adds a flavor of its own for a few bowls and then dissipates over time. Not a bad taste, just different.