More acceptable? Possibly, because Tahitians and akoyas are more valuable than freshwaters generally.
Also, the reason for the dyeing matters. Chocolate Tahitians are made that color to meet a demand for the color. I don't know whether black akoyas predate the culturing of Tahitians, but they probably predate the price of Tahitians dropping to become much more affordable, so they also came into being to meet a demand. They are also darker than most Tahitians I've seen, and of course they are smaller and round. Some people may prefer that look.
Dyed freshwaters are different; they just exist to substitute for significantly more expensive pearls of natural color. As I understand it, it's often the lower quality freshwaters that are chosen for dyeing-- those that didn't make the color grade to be sold as white pearls.
I do not care for dyed akoyas. I do have a strand of baroque dyed freshwaters that I bought loose at a gem show for not a lot of money, back before I owned any Tahitians, and strung myself. I actually like them with certain outfits better than my Tahitians, due to their color range. So yes, I wear them.
Those are the only dyed FWP I have; I don't care for the ones dyed bright blue, green, cranberry, yellow etc. But if someone enjoys them as a bead alternative for hand crafted jewelry, why not?